Ocean Wave Measurement and Analysis (2001)

In this paper a brief review on the nearshore wave breaking processes is given. Various numerical models for calculating the overturning waves are discussed. To account for the turbulence generation and dissipation during the wave breaking processes, the k – ɛ equation model and the LES approach are also discussed.

Five methods of measuring waves in a laboratory setting using video techniques are described. Video observation has several advantages over traditional methods, including a high density of measurement points and lack of interference with the waves. We used off-the-shelf equipment in an ordinary wave basing and obtained excellent results for two of the methods.

This paper introduces a video-based method for directional wave measurement in the physical model setting. The motivation for this study is to provide a non-intrusive method for highly resolved and accurate measurement of wave diffraction in the vicinity of coastal inlet structures. Video observations of wave direction in the diffraction region behind a breakwater structure for three spectra generated by an offshore wave paddle are compared to ADV observations. Initial video-ADV comparisons result in a vector-mean wave direction measurement accuracy within 5 degrees. Experimental results provide a suitable benchmark data set for validation of wave transformation models that incorporate wave diffraction.

We compare PUV wave observations from two collocated velocity/pressure sensors (Aquadopp Current Profiler and Vector Velocimeter). Our objective was to use the differences in the two sensors to evaluate their performance. We evaluate limitations and uncertainties in the wave measurements, focusing particularly on the high frequency cutoff and uncertainties in direction and spreading. We model direction and spreading uncertainties with a simple Monte Carlo simulation, which compares well with our wave data. We conclude that either instrument is able to observe wave spectra and wave height with an uncertainty of a few percent and with wave direction uncertainties of a few degrees.

This paper compares two different methods used for processing bottom PUV data to estimate the kinematics and summary statistics of large surface waves. The first method is based on linear wave theory (LWT). The second method is based on a new approach called the Directional Hybrid Wave Method (DHWM). The PUV data featured in this paper was measured 6 km offshore the mouth of the Columbia River, during fall-winter 1999, in a nominal water depth of 35 meters. This paper examined wave-wave interaction and wave-current interaction to assess the reliability of using linear wave theory and to enhance the utility of bottom PUV data in a water depth of 35 meters. Results of applying LWT and DHWM on PUV data were compared to wave-rider data, obtained from a NOAA buoy 14 km directly offshore from the point of PUV measurement. Results indicate that a current-induced Doppler effect can bias wave estimation by 2–10% and that LWT may have under estimated wave height by 20% during storms. The DHWM appears to offer much improvement over LWT and requires further investigation and verification.

The ability to accurately resolve wave directional distributions in nature is of crucial importance to such applications as port and harbor monitoring, wave climate modeling, and sediment transport. The ADCP Directional Wave Gauge has the theoretical potential for exceptional directional resolution and accuracy. Wave data from many independent deployments seems to substantiate this potential. The goal of this paper is to characterize the ADCP directional resolution, and place it in perspective with other common methods of measuring directional waves. To that end we have: a) Theoretically modeled the ADCP's array and b) Compared the performance of traditional triplet processing, to array processing using a number of simulated directional distributions.

Spatial surveys of nearshore bathymetry and associated velocity fields are essential for many nearshore investigations. A hydrographic surveying system has been designed and tested to acquire nearshore beach profile data. Traditional vessel-mounted echosounder surveying instrumentation was placed in watertight containers and configured for a personal water craft (PWC) for measurements of subaqueous nearshore beach profiles. With the existence of the hydrographic surveying system, an acoustic doppler current profiler (ADCP) was configured onto a PWC to measure nearshore currents. The system is able to withstand the harsh environment of the nearshore and acquire both beach profile information and currents across the surf zone. The system was tested in Sand City, CA during the RIPEX field experiment. The depth-averaged mean cross-shore velocities of the PWC were on the same order of magnitude as fixed instruments, but with a significantly large error (∼20 cm/s). This paper describes the system and results of measurements obtaining nearshore current measurements in rip channels.

The X-band radar was applied to the field observation in the nearshore region. The ocean wave spectra, nearshore current distribution, fluctuations of breaking zone and swash zone, and movement of the local rainfall area were observed with the radar. The continuous images obtained with the radar were analyzed with a method based on the small amplitude wave theory, and the directional wave spectra and nearshore current distribution were estimated. The profile of the estimated wave spectra shows good agreement with that observed at the same time with a wave gage, provings the validity of the radar observation system. Fluctuations of the breaking zone and swash zone were found by using the difference of the microwave scattering intensity between free waves and bores. The radar monitored the individual runup waves, and sighted the breaking points and the top of the swash zone. The radar detected the microwave scattering with raindrops, and tracked the local rainfall area.

A modern directional wave measurement network is operational since 1989 around the Italian coasts. The remote-controlled buoy system is managed by the National Marine Service (SIMN) with excellent results in terms of data acquisition rates, temporal coverage and reliability. This pioneer network and early results of data analysis have been described in previous papers (see references). Recently this permanent system has been upgraded and expanded (from 8 to 14 stations) after a careful revision of either the sensors and the software for signal transmission, acquisition and analysis. The developments of monitoring technology are now calling for faster real-time data distribution and control. The paper aims to inform about the lessons learned during a 12-year management experience, in order to improve the design of similar networks in other countries. Some interesting updated results of data verification and analysis are also given.

Climatic wave spectra for various wave height ranges from long-term wave data measured at five of the National Data Buoy Center's (NDBC) buoy stations in the northern Pacific Ocean were examined. After being normalized, these climatic spectra for various wave height ranges revealed a consistent shape. Minor differences of the normalized climatic spectra among different locations were observed, especially for smaller wave heights. The maximum value of wave spectral energy at each frequency was also examined in this study. An upper limit of the wave spectral energy at the high frequency region was proposed.

This paper discusses wave transformation and correlation methods and results compiled from three coastal projects utilizing southern California wave gage data. Wave transformation of data from the Huntington Beach Array highlights a source of error in the method. Installing future wave arrays in deeper water is suggested as a likely way to reduce this error and expand their applicability. This and other Southern California offshore wave gages were correlated with one another to expand their practical utility over space and time. Correlating data between wave gages is explored as a method to be used as an alternative to or in combination with more traditional wave transformation techniques.

Current-field measurements were done to understand hydrodynamics of low-crested structures (LCS). Drifters were used around a semi-submerged breakwater built in Lido di Dante, Italy to protect a beach nourishment and prevent erosions. Drifter tracks surveyed using radar and nautical compasses are shown together with sea conditions collected during the surveys. The field set up is described. Current patterns are described under the influence of different wave conditions and locations. Results reinforce current knowledge and model simulations.

Within the last years a considerable number of large ships have been lost due to severe sea state conditions. The cause of accidents are in many cases believed to be rogue waves, which are individual waves of exceptional wave height or abnormal shape. In particular steep breaking waves can be fatal for smaller ships. Damage is sometimes also be caused by unusual grouping of waves, which can lead to dangerous ship motion. In situ measurements of extreme waves are sparse with most observations reported by ship masters after the encounter. In this paper a global data set of 5 x 10 km sized synthetic aperture radar (SAR) images acquired by the European Remote Sensing satellite ERS-2 every 200 km along the track is used to analyse extreme ocean wave events. As the European Space Agency (ESA) does not provide this dataset as a standard product wave mode raw data were reprocessed to complex SAR images using the processor BSAR developed at the German Aerospace Center (DLR). About 1000 globally distributed SAR wave mode images are available every day. Two dimensional ocean wave fields are derived from SAR images by inversion of the SAR imaging mechanism. Individual high waves are detected in the derived wave fields using a matched filter technique. Grouping of waves is studied using wavelet techniques. Statistics are presented on wave group size and frequency. The inhomogeneity of ocean wave fields is anlysed using a parameter, which describes the shift invariance of the wave spectrum.

JERICHO is an interdisciplinary research project (within the BNSC LINK programme) which has investigated the application of the wave measurements from satellites, with shallow water wave models, to the strategic planning of coastal defences. JERICHO has been primarily a scientific project, but was directed by the practical strategic requirements of the Environment Agency (EA), who were a full participant in the project. The design of sea defences, such as sea walls, groynes and revetments, to provide protection to the livelihood of people living close to the coast, requires a good knowledge of local wave, tide and beach conditions. Of these factors, it is the local inshore wave conditions that have, perhaps, the most uncertainty. Long term wave recordings are scarce and so offshore conditions are often determined from the output of numerical wave prediction models using predicted wind fields from numerical forecast models. However, good quality in situ wave measurements covering extended periods of more than a month are extremely scarce. Moreover, making such measurements can be an extremely expensive undertaking. The search for alternative sources of wave information has prompted the use of: observations from ships; output of wave prediction models and latterly, satellite-derived measurements. These sources usually provide information about waves in deep water some distance away from the site of interest. In order to make use of such information it is necessary to be able to transform the offshore wave climate to the shore. There are a number of methods available for wave transformation. Here, a wave refraction model is used as the site of interest, Holderness, is on open coast with an evenly shoaling seabed. The same approach has also been used in a study to investigate the use of synthetic wave data from a global operational wave model for flood warning. Establishing the accuracy of using deep-water waves (whether measured or simulated) and a wave transformation model instead of in situ measurements is important from two perspectives. Firstly, if the transformation of deep-water conditions is sufficiently accurate it provides an economic and accessible means of determining inshore wave conditions. Secondly, it provides the scope for including the effects of climate change, such as increased wave heights or storminess, into the design and management of coastal schemes.

This paper examines the problem of global wind speed retrieval from satellite altimeters and demonstrates the existence of sea state induced biases. A new dataset of collocated Topex/ buoy measurements is used to validate four existing altimeter wind speed models based on formulations of the nadir backscatter used either alone or in combination with altimeter significant wave height. Evidence of sea state induced biases in the retrieved wind speed is presented using a variety of sea state discrimination criteria, including those of open/enclosed seas, fully-developed seas and wave age. We find that all existing models show a residual dependence on wave age, which leads to altimeter underestimating winds by 1 m/s on average in the case of young seas. Sea state effects at nadir are shown to produce both seasonal and regional biases in the altimeter-derived wind speed climatologies.

Distribution characteristics of wind and wave near centers of typhoons were analyzed by using satellite data. Many characteristics have been newly found. Wind speed, wind direction and wave height depend very strongly on the relative position based on the center of the typhoon.

In this study, we present analysis of the Fourier harmonics from decomposing the directional spectra derived from three-dimensional ocean surface wave topography by an airborne scanning lidar system. The similarity properties of the wavenumber dependence of Fourier coefficients are analyzed. A nonlinear function is proposed to represent the similarity relation. A bimodal directional distribution model in the form of Fourier series expansion consisting of the first eight Fourier harmonics is developed. Application of this model to directional buoy measurements is demonstrated.

A parametric inversion scheme for the retrieval of two dimensional ocean wave spectra from look cross spectra acquired by spaceborne synthetic aperture radar is presented. The scheme takes information about the spectral shape of the different wave systems from a prior wave spectrum, while estimates for wavelength, waveheight and wave propagation direction are extracted from SAR cross spectra. The Partition Rescaling and Shift Algorithm (PARSA) is based on a partioning of a prior wave spectrum, e.g. taken from ocean wave models. For each ocean wave system a stochastic model is set up, which defines the probability that the propagation direction, the wavelength or the energy of the different wave systems deviate from the prior knowledge. The prescribed probabilities thereby quantify the confidence into the prior wave spectrum. Based on the probability models for the prior wave spectrum and the measured cross spectrum an optimal ocean wave spectrum is estimated using a maximum a posteriori approach. To solve the corresponding minimization problem the prior model is approximated with a multivariate Gaussian model. The optimization problem is solved with a Gauss Newton method. The scheme is tested using both simulated cross spectra and reprocessed wave mode data acquired by the ERS-2 SAR. The reprocessed data are similar to the products, which will be available from the ENVISAT satellite to be launched in 2002.

EuroROSE ("European Radar Ocean Sensing") is an EU funded project (contract no. CT98-0168). Its main aim is to demonstrate to end users (port and coastal authorities, VTS centres, etc.) the capabilities of wave and current monitoring by using radar systems on shore. As a task of the project, a graphical user interface has been developed. This software has been designed to be a real time monitoring application for oceanographic and meteorological data. The source code was developed taking into account the necessities, recommendations and remarks of the end users.

A class of models, termed Boussinesq wave models, has been developed in the past to provide time dependent (phase-resolving) wave information for shallow and intermediate water depths. Recent extensions include wave breaking, runup and expansion into deeper water. There is a need for appropriate field data (spatial and time dependent) to control, calibrate and validate the models. Spatial quasi-continuous measurement techniques using high resolution digital cameras are applicable for this purpose. The research area is a groyne field on a North Sea island in Germany. First results are presented.

The objective of the EuroROSE project was to combine area covering ground-based remote-sensed wave and current data with high resolution numerical forecast models to provide now- and forecasts for coastal marine operators. The first experiment to test and demonstrate the system took place on the coast of Norway, north of Bergen in March 2000. Qualitative and quantitative intercomparisons of the wave measurements and wave model products from this experiment are presented. These include measurements using the WERA HF radar, the WaMoS X-band radar, a directional waverider and output from the WAM wave model. Comparisons are made of the full directional spectra and of various derived parameters. This is the first ever intercomparison between HF and X-band radar wave measurements and between either of these and WAM.

Measuring the sea surface currents by HF radar has already reached the practical level. Many observations have been done in the costal zone, and it has gotten great results so far. On the other hand, measuring the ocean waves by HF radar is not in the practical level yet, is actually in the theoretical level. The directional wave spectrum can be recently estimated from Doppler spectrum by the method which Hashimoto and Tokuda proposed theoretically. The directional wave spectrum, however, cannot always be estimated from Doppler spectrum by this method because the noise is contained in the received signal and Doppler spectrum estimated from the received signal is different from it in the theory. This study numerically simulates the received signal containing the noise and makes it clear what kind of influence is in Doppler spectrum calculated from it. In addition, it is evaluated that the influence of the noise to the directional spectrum estimated from Doppler spectrum, too.

WaMoS II is an operational wave monitoring system based on a standard marine X-Band radar generally used for navigation and ship traffic control. The system was basically developed in the 80' ties and is commercially available since 1995. WaMoS II can be operated from fixed platforms as well as from moving vessels. The system is type approved by Det Norske Veritas for the use on board ships travelling with up to 40 knots. In this paper operationally collected WaMoS II wave data are compared to conventionally measured wave data. The measurements are from a deep water off-shore oil platform (Ekofisk, Norway), from an oil shuttle (Navion Oceania, Norway), and from a shallow water coastal station (Helgoland, Germany). For the main sea state parameters, such as significant wave height, peak wave period and peak wave direction, error statistics are applied. Within MaxWave, an EU project funded under the 5^th framework programme, a new method to obtain single wave information from nautical radar images will be developed. Here a method to derive partial wave information from nautical radar images is presented. Phases of partial waves are derived from single pixel. This spatial varying information, represents the local variability in the observed wave field. The resulting phase maps show significant wave crest patterns. These wave crest patterns exhibit the modulation of the ocean waves as they propagate through the observation area.

The microwave signature of the ocean is important to the remote sensing community because it contains information about surface wave field properties that can be used to estimate atmospheric forcing effects. Experimental studies of the transformation from the received microwave backscatter into a surface wave spectrum have been limited by our ability to adequately measure in situ ocean surface wave properties in the short gravity and gravity-capillary regions. A new instrument was developed to study the directionality of short gravity and gravity-capillary waves for the purpose of ground-truthing microwave scatterometer measurements. It was deployed as part of an experiment along with an azimuthally rotated scatterometer, a sonic anemometer, and a six-element capacitive wire wave gage were deployed at the test site. The resulting data from the wave wire buoy show that the measured frequency spectrum slope and wavenumber spectrum slope agree with various models in the literature. There is additional agreement between the measured width of the spectra collected with the wave wire buoy and the azimuthal width of the scatterometer return. However, it was found that the widths of the scattered return predicted by current wavenumber spectral models were consistently larger than those measured by either the wave wire buoy or the actual scatterometer.

This paper compares simultaneous microwave radar and video camera signals from shallow water breaking waves. The results show that the radar cross section (RCS) is well correlated with the size of the turbulent breaking region estimated from the video camera. This indicates that microwave radar is a good breaking wave detector and can be used for the measurement of the spatial and temporal variations of wave breaking. In addition, microwave radar offers the advantage of not being sensitive to relict foam generated in the breaking process. Finally, the RCS per unit area of the turbulent breaking region appears to be well approximated by a constant value of –2 dB (± 0.5 dB).

This paper illustrates a method of calculating bathymetric maps of shallow water areas (<20m depth) using an analysis of wave properties determined from an analysis of marine radar image sequences of waves. Water depths determined using this corrected for tidal variation in water level are compared quantitatively to conventional surveys. Two case studies are shown from the COAST3D project field sites at Egmond aan Zee in the Netherlands and at Teignmouth in the United Kingdom.

A fundamental barrier to consequential evaluation of modern, very capable shoaling wave and surf models has been the inability to provide high-quality ocean data with which to test model results. This paper describes a development intended to satisfy this need by providing a time series of visible images of the nearshore from which three parameters crucial to such evaluations are simultaneously retrieved, namely the 2-D fields of the directional wave spectrum, bathymetry and currents. In addition, the images provide direct information on where the breakers occur, thereby furnishing critical data for comparison with model results. A digital camera-based imaging system has been constructed, mounted on a small aircraft and used to collect long sequences of images of waves as they shoal and break. The fields are retrieved using recently developed algorithms that operate on space-time variations in the images. The results are evaluated by comparing the retrieved fields with in situ data collected at the U.S. Army Corps of Engineers Field Research Facility during the SHOaling Wave Experiment (SHOWEX).

A series of experiments were conducted to determine if wave fields in hydraulic models could be measured with Phase Profilometry. Phase Profilometry uses the distortions of periodic shadows to measure surface topography. The wave fields were photographed using a vertically-looking digital video camera operating at 30 frames/s. Several methods for making the water opaque were evaluated to insure reflection of the shadow pattern. A specially developed algorithm was used to analyze each frame of the digital video and deduce the topographical history of the wave field. A comparison was made between wave height histories measured by Phase Profilometry and by a capacitance wave gage. There agreed within 5–7%. These results are presented as well as an analysis of the accuracy of Phase Profilometry for wave field measurements. We conclude that Phase Profilometry is a practical remote sensing method for measuring surface wave field topographical histories for many applications, and is a significant improvement over the current practice of measuring surface wave histories at discrete points using intrusive methods.

This work presents a new spectral technique for analysis of data from wave directional sensors. It is well known that one of the main problems in directional analysis is a poor spatial resolution due to the small number of sensors. The new technique can provide better resolution by detecting the occurrence of certain events along a record, i.e., waves of a given frequency range propagating in a well defined direction. The combination of these events allows for the computation of the energy directional distribution, D(θ), as well as for the values of spread for different seas and, at last, the directional spectrum. Some examples of wave climate of the Campos basin off Rio de Janeiro coast using this technique are shown.

The paper discusses the impact of second order wave spectra on heave/pitch/roll wave measurements. It is found that the sharp increase of the directional spread and the check ratio below the spectral peak may be explained by the 2nd order spectrum. Sum-frequency contributions turn out to be of negligible importance.

Interactions among free waves result in bound waves, which may significant affect resultant wave properties in an ocean wave field, especially when waves are steep. Since the measurements record the resultant properties, the presence of bound waves makes it inaccurate to analyze the measurements of steep ocean waves using linear spectral methods. To overcome this difficulty, Hybrid Wave Models (HWM) developed recently, separate bound waves from free waves in the decomposition of an irregular wave field as well as the prediction of its resultant properties. To ensure the convergence, the HWMs selectively use the conventional and phase modulation approaches to address the nonlinear interactions between free waves of different frequency ratios. The models are able to decompose a wave field accurately and hence can predict the wave properties accurately and deterministically based on the time-series measurements. Examples of their applications to the analyses of laboratory and field measurements are given to demonstrate the usefulness of HWMs.

A new method for the estimation of directional spectra is outlined and illustrated with data from an array of wave gauges. The method employs wavelet analysis techniques and thus is well adapted to dealing with non-stationary data. The product of this analysis is the wavenumber directional spectrum, which is of fundamental value to a host of applications of knowledge of the wind-driven ocean surface. Since the basic data are time series from each gauge in the array, frequency direction spectra may also be obtained.

Techniques are developed to estimate directional wave spectra from point measurements made by non-stationary wave sensors. Examples of data sources are: (1) several freely drifting small wave buoys potentially deployed from aircraft, and (2) one or more wave measuring Autonomous Underwater Vehicles (AUV's) moving in programmed paths. All sensors are time-coordinated and each sensor's horizontal position is adequately established using Global Positioning System (GPS) methods. Sensor paths are assumed to remain within a zone of wave pseudo-stationarity. Procedures for sensors that are moving relative to each other are based on time domain statistical procedures utilizing stepwise, ridge regression with random selection of candidate transfer functions over a frequency/direction search block. Simulated data are used to illustrate results for pressure sensors mounted on AUV's. The techniques are also applicable to fixed-position sensor arrays currently in use.

Accurate estimation of JONSWAP parameters provides essential information for initial planning and design of coastal and ocean structure, as well as for later design modification or alternatives that could bear on either mitigation or environmental changes or enhancement of other aspects of the environment. Based on the demand of reliable field wave measurement, an oceanography observation network, which consists of 6 buoy stations around Taiwan. In present study, it is the purpose to obtain the JONSWAP parameters from the observation stations. It is found that different parameter sets might give similar spectral shapes due to the fact that there is high dependency between parameters α and γ. On the other hand, various values of the parameters will be obtained depending on different data fitting procedures. The differences of the parameter values range up to 15%, which should not be neglected. At last, the γ of the winter monsoon waves is from 1.44 to 1.69 in the western coast, and 2.09 to 2.66 in the eastern coast.

Water surface elevation, η(t), is often measured in marine field experiments and research facilities with echo ranging gauges. Proper operation of these gauges requires judicious setting of the receiver circuit to prevent data drop-outs. Field experiments, where the sensors are left unattended for long periods of time, are particularly susceptible of data drop-outs as metocean conditions affect the reception of the echo signal or the pre-selected range of measurement changes. When the amount of data collected is small, user interactive software featuring simple interpolation methods allows for replacing data drop-outs relatively quickly. However, these are slow when the amount of data collected is large. An automated data smoothing method has been developed implementing B-splines. The software derived from this implementation was tested for accuracy using random wave records measured during experiments at the O.H. Hinsdale Wave Research Laboratory at Oregon State University. In the experiments, η(t) was recorded with two ultrasonic wave gauges. One was carefully set to record realizations free of data drop-outs and to be used as targets. The other gauge, not so carefully set, recorded data with drop-outs that were smoothed using a) a user interactive software and b) the automated software. The data "drop-out free" records obtained after smoothing were compared to the target records by means of cross correlation analysis. Records smoothed with the automated software showed the same or better correlation to their corresponding data "drop-out free" records than records smoothed with a user interactive software by visual inspection.

In recent years, there have been new suggestions for recovering surface wave from underwater pressure transducer, such as the ones by Kuo and Chiu and Hashimoto et al. This study compared these methods with the widely used pressure transfer function from linear wave theory, using field data measured by an ultrasonic wave gauge. From the measured data it was found that the two new methods did not improve the accuracy on the surface wave reconstruction.

The rainflow filter is a nonlinear filter which can be used to eliminate small-amplitude oscillations in a signal. An advantage of the rainflow filter, well known in applications to fatigue, is that a considerable reduction of data is made, while the calculated total damage is not affected. An approximation of the filter in the form of a transfer function can be obtained from spectral simulations. To validate the so derived filter, the capability of filtering out small cycles is examined. Further, we pay attention to calculation of distributions for characteristic wave parameters. These methods need as input a spectral density, where high frequencies often are cut off. Numerical examples indicate that the rainflow filter is advantageous to use when filtering records of sea-elevation.

The Empirical Mode Decomposition (EMD) method for nonlinear and non-stationary time series analysis, also known as Huang Hilbert Transform (HHT), is applied to wave field data from the nearshore area. The frequency-time distribution of the energy, designed as a Hilbert spectrum is utilized for examination of the group structure of the sea waves. The necessary condition for existence of wave grouping is determined on the base of the results of empirical mode decomposition of the data. The HHT method provides a unique basis for expansion of the data, derived from and based on the data. The variations of the group characteristics across the shore are examined and their relationship with the local wave characteristics is investigated outside and inside the surf zone. The Hilbert spectrum provided new insights on the wave and group transformation in the cross-shore direction.

An existing analysis technique for separation of incident and reflected wave trains is extended towards a 2DH formulation, for constant depth. Combined with a phase-averaged technique (MLM), a phase resolving analysis of multidirectional wave trains is performed. The ability of the algorithm to separate directional components in a short-crested sea is tested against a numerical simulation and a laboratory observation of a short-crested wave field. The investigations show, that the directionality of a short-crested wave train can succesfully be approximated in a phase resolving manner, by a superposition of multiple long-crested waves, propagating in various (main) directions.

The National Data Buoy Center (NDBC) began posting buoy estimates of swell height and period in 1997 because of numerous requests from mariners. Until then, only significant wave height, dominant period, and spectral wave data were posted on its Web site. Though swell information can be gleaned from the wave energy spectral, many mariners do not have the time or experience to do so. NDBC developed a method based on wave steepness that requires only nondirectional wave data. This method determines a period to separate the wind seas from the swell based on the knowledge that seas are steeper than swell and that maximum steepness occurs near the peak period of the wind waves. However, the method underestimates the swell when winds are light or abating, as compared to the Navy's operational wave model (WAM). To improve performance, the steepness method was modified to limit the maximum allowable separation period based on the observed wind speed. Since peak frequencies of fully developed seas generated by a given wind speed are well known, this relationship can be used to set an upper limit on the separation period. Positive results were obtained in tests of the modified method using measurements from directional buoys where swell and wind seas can be easily identified by differences in propagation direction. The modified method also compared much more favorably with wind sea and swell estimates from the WAM.

The results of estimating the directional wave fields in front of a detached breakwater were compared here in this paper. Two of the non-phase-locked methods, i.e., the Maximum Likelihood Method (MLM), and the Extended Maximum Entropy Method (EMEP), were adopted for the purpose. Although the latter outperforms the former in estimating directional spectra, the improvements for estimating the reflection coefficients just in front of the reflector are only marginal. It is shown that the reflection coefficients decrease with the increasing distance away from the detached breakwater. The more spread is the directional distribution of the wave field, the more energy will diffract into the lee of the detached breakwater.

One of the useful measures of wave directional spreading at a given location is the directional spreading parameter. This paper presents a new approach to arrive at its characteristic value using the computational technique of Artificial Neural Networks (ANN). Different networks were developed in order to obtain the characteristic spreading parameter from the unidirectional parameters of significant wave height and average zero cross wave period, Ursell number, spectral width, spectral peakedness and maximum spectral density. An ANN was also developed to get the spreading parameter from the directional width. Training of the networks was trained using alternative algorithms. The data used belonged to a site off Goa along the west coast of India. The network output compared well with the target spreading parameter values. Use of alternative training was some times found necessary to get accurate output. The spreading parameter was more strongly correlated with characteristic wave height and period — in either individual or grouped form — than the unidirectional spectral characteristics.

A formula for the significant wave period is derived. This containes the complex value integral of energy spectrum, and thus depends on the spectral shape asymetry. For the wind waves characterized by a Pierson-Moskowitz spectrum the spectral asymetry becomes remarkable, so that the significant wave period T_1/3 deviates from the mean period T_m. The empirical ratio T_1/3/T_m of 1.2 is well interpreted by the proposed theory.

Analysis and interpretation of wave measurements must usually be separated into two general routines: short-term statistical analysis of single wave measurements and long-term statistical analyses of wave measurements representing a longer period. The available input data and the methods chosen for the statistical analyses have an important influence on the expressiveness of the results and the application of the derived wave information for practical engineering problems. In the paper selected aspects of the short — term and the long — term statistical analysis of wave data will be dealt with. These will mainly cover the required data base for the statistical analyses and the influence of the frequency of the sampled data on the results of wave data analyses.

The sea state severity is commonly presented in form of bivariate histograms of significant wave height and the mean zero-upcrossing wave period. Since there is no known theoretical basis for choosing any particular distribution, various statistical models have been proposed to characterise the bivariate distribution of these parameters. The adequacy of a statistical model requires some test to evaluate the goodness-of-fit of the model to the sample data. A two-dimensional version of the classical Kolmogorov-Smimov test, which is distribution-free for practical purposes is described in this paper. This method is illustrated by fitting the empirical distribution of significant wave heights and average zero-upcrossing periods of wave data measured in the Norwegian continental shelf to the Plackett model.

Applicability of the extreme value analysis model calculating the parameter with the least square method (LSM) for a censored sample is investigated through a large scale Monte-Carlo simulation. The study shows that the LSM model with a jackknife method may yield under- or over-estimation for either the return value or its variance in the upper and double censoring cases with smaller sample size, whereas the model gives rise to precise estimates in the lower censoring and uncensored cases. Also, analyses for the measurement samples with different types of missing data reveal that the LSM model may produce an estimate of the return value comparable to the maximum likelihood method (MLM) model for a censored sample but a greater variance of the return value. This indicates that the LSM estimate is statistically less efficient than the MLM estimate.

The connection between extreme waves and nonlinear group formation is described. A statistical relation is shown, and a physical explanation based on nonlinear dispersion is investigated. Theoretically it can be described by the modified nonlinear Schrödinger equation. Here a simplified theoretical approach is made, in order to interpret laboratory experiments. The results show that the balance between the energy envelope and the instantaneous frequency is essential. Extremes from experiments with random waves show a behaviour similar to effects in bichromatic wave trains.

This paper addresses nonlinear effects in successive wave crest height statistics. Two methods are used to derive joint distribution functions of successive wave crest heights. The first model contains second-order Stokes type nonlinearity, while the second is a parametric model based on second-order simulations. Comparisons are made between the two models. Analysis results of data from field measurements in the central North Sea are also included in order to evaluate the models. The nonlinear effects observed in the data are well predicted by the models.

This paper deals with the appearance properties of large wave heights in storm. Several wave data obtained in the Japan Sea are analyzed to investigate the properties of wave height. A simple simulation method of random wave in storm is also proposed for the purpose of the supplementing the wave data. The energy spectrum of wave, the significant wave height and period are used to simulate the random waves. This simulation method is applied to estimation of the characteristics of large wave heights at other wave observation points.

Stokes 5th-order wave theory is used to modify the Rayleigh probability law for random deep-water waves. Results show that predictions differ sensibly from those based on 2nd-order theory for high waves in heavy seas where crest amplitudes equal or exceed the significant wave height and where wave heights equal or exceed twice the significant wave height. Predictions are shown to be in good agreement with published field measurements.

Seafarers have traditionally reported that under heavy seas, a rapid increase of wind force tends to reduce the height of the waves. This phenomenon is at variance with common scientifically-accepted ideas of the behavior of wind waves, since the wave height in a wind sea increases with wind speed, the rate of wave growth increases with wind stress and with sea-surface roughness, and wave breaking, which should increase during severe wind conditions, tends to increase the sea-surface roughness. However, it has been shown, for example by Banner and Phillips, that a vertically-sheared current reduces the maximum steepness a water wave can have before breaking, Since the shear in the surface current will respond more rapidly than the wave height to a sudden increase in wind speed, an increase in the intensity of wave breaking should then occur, leading to a temporary decrease in wave height until the sheared current distributes itself through the water column. The simple model described in this paper reproduces this effect, although the reduction in the wave height is predicted to be rather modest, of the order of 5 per cent. Although it is applied for deep water, the results are consistent with the laboratory observations of Douglass on the effect of on-shore and off-shore winds on nearshore wave breaking.

Laboratory observations by others have shown that a following swell reduces the net growth of wind waves whereas an opposing swell enhances this growth. Computations show that third-generation wave models based on the commonly accepted WAM-III formulations do not reproduce these effects for following swell. For opposing swell they do, but this seems to be fortuitous. With some relatively simple modifications of the formulation for the generation and dissipation of the waves, both observed effects can now be reproduced. The modifications for the generation by wind consist of replacing the driving wind by an apparent wind (which depends on the swell orbital motion) and by scaling the wind input with the swell orbital motion. For dissipation (whitecapping) the modification consists of decoupling the whitecapping at high frequencies from the wave steepness at low frequencies.

Intermediate results of ongoing research at NCEP to improve the accuracy and economics of wave propagation in large-scale wind wave models are presented. The main attention is focussed of new solutions for the so-called Garden Sprinkler Effect. Also briefly discussed are the need for higher spectral resolution and plans to deal with unresolved islands by sub-grid treatment rather than by increasing spatial resolution.

Directional wave spectra derived from a data set measured off the west coast of New Zealand are used to investigate the directional spreading within swell. The location where the measurements were made is particularly useful for the study as a more or less constant swell component originating from the Southern Ocean is observed in the sea states. The spectra are partitioned into wind-sea and swell components, and estimates of the directional spreading of the swell component is made. A function for the directional distribution of the swell is proposed.

We examined the validity and the effectiveness of the DIA on the basis of the accuracy of the computations of the nonlinear energy transfer for various directional spectra. Then, we proposed new methods, an extended DIA (EDIA) and a modified DIA (MDIA). The optimum parameters included in EDIA and MDIA were properly adjusted by minimizing the errors between the exact values and their approximate values for various directional spectra. The efficiency and accuracy of the EDIA and the MDIA were examined for various directional spectra and computational conditions.

This paper introduces a method to extend the Discrete Interaction Approximation for the computation of quadruplet wave-wave interactions in wind wave spectra. This is achieved in two ways. First, by introducing a generally shaped configuration between the four interacting wave numbers in a quadruplet for which the corresponding equations to compute these non-linear interactions in a wave spectrum are derived using the principle of detailed balance as starting point. Second, by adding additional wave number configurations. By using a kind of orthogonal expansion of generally shaped wave number configurations it is possible to approximate the exact solution to any desired degree of accuracy.

The activities of the WAM (WAve Model) and the WISE (Waves In Shallow-water Environments) groups have accelerated our understanding of the physics and numerics of waves in shallow water. Two third generation numerical wave models, namely, the WAM which has been extended to coastal areas and the nearshore wave model SWAN (Simulating WAves Nearshore) which replaced the HISWA (HIndcasting Shallow water WAves) model are implemented in the shallow water of Lake Erie of the Great Lakes with water depths varying from about 5 m to 50 m. The primary purpose of this study is to examine the performance of the WAM and the SWAN running in shallow water mode and using wind forcings provided by a numerical weather prediction model. The two models are run for selected periods and the results are verified against buoy measurements and the operational forecasts from the RCTB (Regional Centre of Thunder Bay) of Canada. This allows an assessment of the performance of the two models and the effect of shallow water on wave forecasting with a view towards operational implementation of either the WAM or the SWAN model, or both, on Lake Erie.

The wave growth limit in shallow water is studied by analyzing a) field data from two Dutch lakes, b) the wave growth curves according to Bretschneider and Young and Verhagen and c) the results of the numerical model SWAN. The uncertainty about the achievable wave height to water depth ratio appears to be considerable. SWAN tends to underestimate the wave growth limit and a strategy for further model improvement is pointed out.

In the present study a method to improve wave forecasts with data assimilation is developed. To use it in operational conditions the method has to be both efficient and effective. To be effective variational data assimilation is used. To be efficient only a small number of control variables is used based on clusters of wind vectors in the computational domain. Five different methods have been investigated for the clustering. These have been tested in a series of experiments on different oceans and with different observation sets (buoys and ERS-2 and TOPEX satellite observations). The results of the tests showed little improvements in the wave forecast, which is probably caused by the high quality of wind fields in the experiments.

SWAN model predictions of wind generated waves are validated with experimental data for a large shallow lake named `IJsselmeer'. Both global scatter plot comparisons and in-detail case studies were used for the model validation. Wave heights were well predicted except in conditions of strong depth-induced breaking. SWAN's performance with respect to wave spectra was a mixed bag whereas wave periods were consistently underestimated. The latter is probably due to imperfect modelling of the four-wave-interactions. Finally, much attention was given to the convergence behaviour of SWAN, which was improved by using the experimental version SWAN40.16.

Global wave predictions produced at two U. S. forecasting centers, Fleet Numerical Meteorology and Oceanography Center (FNMOC) and the National Centers for Environmental Prediction (NCEP) are evaluated with spectral buoy measurements. Previous validation studies of global wave models were based primarily on wave height data from operational satellite altimeters and moored in-situ buoys. Fewer comparisons of frequency spectra and directional wave properties have been reported. In this study, data from directional wave buoys are used to examine the fidelity of frequency-directional spectra predicted by WAM and WAVEWATCH III (WW3) at the operational centers. The buoys used in the comparisons include 3-meter discus buoys operated by the National Data Buoy Center (NDBC) and Datawell waverider buoys deployed primarily along the California coast by the Scripps Institution of Oceanography Coastal Data Information Program (CDIP). Only buoys located in deep water are used in the comparisons. Here, preliminary results are presented for two locations, Point Conception, California and Christmas Island. Model nowcasts of frequency spectra and mean wave direction are compared to buoy measurements over a six-month period from 01 October 2000 to 31 March 2001. Individual swell events were identified in the spectra from the three models and the buoy data. Predicted and observed swell frequencies and arrival directions are compared, as well as the total energy transported past the buoy over the duration of each individual event. Two separate implementations of the WW3 model generally outperformed WAM.

For the determination of protection standard afforded by an existing or recharged beach extreme wave parameters may be needed. The long term behaviour of beaches and dunes, however, is more dependent on the regional wave climate, which e.g. allows to predict the overall longshore movement of beach material. The wave direction in this context is the most sensitive parameter. Up to nowadays wave hindcasting models were the most reliable source for wave directional information. Nowadays directional wave recording are a reliable tool to determine deep water wave climate and to perform investigations on a site-specific basis. Wave directional wind and water level recordings over a period of 15 years and their interrelations are used to describe a concept of setting up a long term hindcasted nearshore wave data base (50 years) in form of hourly directional wave parameter information. Besides applications of the data for the purposes of structural design and for the longterm maintenance of a coastal region are outlined.

This paper describes the wave measurement and numerical modeling components of a regional monitoring and modeling system established for the south shore of Long Island, New York. The monitoring portion was begun in April 1998 and has produced a wealth of data on waves, currents, water level, and soundings at inlets. A directional spectral wave model incorporating nested grids with fine resolution at inlets provides an efficient and accurate means of calculating nearshore waves. Validation of the modeling system is presented, together with discussion of the managerial functions of the data and model.

Current design criteria for shore protection and flood control structures on Lake Erie are based on the assumption that the return periods of storm waves and elevated water levels are independent. This criteria was examined since both wave height and water levels are influenced by wind speed and direction. An analysis of 32-years of WIS hindcast information (1956–1987) and measured lake water levels (1956–1987) illustrated the inter-relationship of storm waves and lake water levels. A database and qualitative assessment of the relationship between wave heights and water levels was developed for four locations on Lake Erie (Buffalo, NY; Erie, PA; Cleveland, OH; Toledo, OH). Only the Buffalo location is presented herein. The EST (Empirical Simulation Technique) program was used to develop return period information incorporating the natural inter-relationship of wave heights and water levels. These results are used to assess the current design methods.

The determination of design wave height is fundamental to most coastal and ocean engineering applications. While the design wave height analysis and selection may appear to be a straightforward and routine analysis, significant discrepancies in results can occur based on the original data source used as well as extremal analysis techniques utilized. The availability and quality of wave data for use in coastal and oceanographic studies is a common initial hurdle for most applications. If wave data is available at all, it can be available in a wide variety of forms and periods of record. This paper will investigate the implications of the various wave data sources on resultant design wave climate determination. Extremal analysis techniques are also evaluated. Results presented herein show that reliance on deepwater buoys to define transitional depth wave climate may underestimate extreme wave heights. Wave Information Study Phase II data provide lower design wave estimates by as much as 3 to 4 meters. Nearshore wave estimates along the Oregon coast are higher by 3 meters compared to the northern Oregon coast. Selection of the storm threshold in the Peak-Over-Threshold method of extremal analysis significantly affects the results.

Satellite and model climatologies of monthly mean wave height are compared globally and in the North Atlantic. All of the tested climatologies give a broadly consistent picture of regional variations in wave climate. There are however some systematic biases between climatologies and all the climatologies are subject to root-mean-square (rms) errors of the order of 0.1 meters or more. The global model climatology (WAM-ERA) is marred by large errors in some regions, and by a general tendency to underestimate large waves and overestimate small waves. Errors in climatologies based on a single satellite result primarily from sparse sampling and are largest where variability within a calendar month is greatest. A model of the North Atlantic (AES-40) is largely consistent with the satellite measurements, and the estimated rms errors of this model are less than the estimated satellite errors in the stormy northern North Atlantic of the winter period.

The Wave Information Studies (WIS) at the U. S. Army Engineer Research and Development Center (ERDC) currently works on improving wave hindcast information for the Great Lakes. WIS has previously conducted the Great Lakes hindcast for 1956–1987. A recent update only covers Lake Michigan for 1988–1997. These hindcast studies were based on the deepwater wave modeling assumption that no shallow water effects were computed. Examining the previous hindcast results has shown notable bias in both wave height and period estimates. The bias is primarily caused by the poor quality of wind input information used in the hindcast. The present study is aimed at improving the wave hindcast using the newly generated wind field information that is considered to be more accurate and consistent in the long-term application. It is shown that to include shallow-water effects in the wave modeling is critical leading to accurate hindcast in the nearshore area.

A long-term wave hindcast system which consists of the ECMWF wind data sets over a period of 20 years from 1979 to 1998 and a shallow water wave model based on backward ray tracing is applied to the estimation of year-long waves at each of almost all measurement stations deployed around the coasts of Japan. Comparison between 2–3 hourly measurement and hindcast is made for a time series of waves, wave climate parameters of each month or over the whole period, their climatic change and extreme wave height. One main finding is that the system is very useful not only for a proper evaluation of the wave climate and its interannual change but also for a first guess of the return wave height with confidence interval at any coastal location around Japan directly facing the open sea, particularly on the Japan Sea coasts.

A procedure to blend wind fields obtained from NCEP's operational AVN global atmospheric model and GFDL hurricane model for single and multiple tropical cyclones over the ocean has been developed. Blended wind fields are used in NWW3 wave model for predicting Western North Atlantic waves during the hurricane season of the year 2000. The resulting products, both winds and waves, are compared with data obtained from instruments on NDBC buoys. It shows that using blended wind fields provide more realistic wave fields over the areas within hurricane influence than just using AVN winds only.

Wave-buoy data collected off the coast of the US Pacific Northwest (Washington and Oregon) document that significant wave heights and periods have progressively increased during recent decades. The average deep-water significant wave heights during the "winter" (October through March) have increased at a rate 0.032 m/yr from 1978 through 2001, a 0.77-m change, while the increase in wave heights associated with the strongest storms has been even greater. Calculated swash runup levels on beaches, which depend on both deep-water wave heights and periods, show parallel increases; the rate of increase has been 0.010 m/yr, which would have produced more than a 6-m landward shift in the mean shoreline during the winter since the late 1970's. Such decadal trends, together with extreme-value analyses of deep-water wave parameters and swash runup levels, are being used to assess the potential for future beach and property erosion along the Pacific Northwest coast.

This paper describes the mathematical formulation and application of a linear refraction-diffraction model for steep bathymetry. The model involves two coupled governing equations derived from Green's second identity. It reduces to the extended and original mild-slope models, when the seabed slope is small. The capability of the present model to simulate flow velocity and wave amplitude over steep island bathymetry is examined. The computed results are compared with the original and extended mild-slope solutions and verified with those of a three-dimensional wave model. The present model has the same data requirements as other two-dimensional models, but provides more accurate and realistic three-dimensional results.

A method for estimating the reduction of wave energy in shallow water from knowledge of wave spectra in deep water is developed through the stochastic process approach. The loss of energy associated with shoaling and breaking is evaluated along with consideration of the change in wave characteristics from Gaussian (in deep water) to a non-Gaussian (in shallow water) random process. The methodology consists of the evaluation of energy loss in three areas; shoaling zone, breaking point and surf zone. The breaking point in a random sea is defined from consideration of the probability of breaking and energy loss.

Conventional absorbing boundary conditions used in elliptic harbor wave models usually do not consider the effect of incident angle and amplitude variation of the outgoing waves at a boundary. In this paper, a generalized absorbing boundary condition with linear approximation is developed to account for these effects. Improved solutions have been obtained using the new boundary condition in three test cases that show little spurious boundary reflections. The proposed boundary condition increases the reliability of model predictions for complex real-world applications.

A time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter using the Taylor series technique. On horizontally one-dimensional case numerical tests are made for regular waves over sloping beds and also for regular or irregular waves over a ripple patch. Numerical results prove that the present model gives accurate results for not only regular but also irregular waves over rapidly varying topography.

Field measurements and laboratory investigations were performed on an impermeable dike and the corresponding shallow foreshore. At this site storm conditions and wave run-up levels were measured by Rijkswaterstaat. Two-dimensional physical model tests were performed by WL | Delft Hydraulics and three-dimensional physical model tests were performed by University College Cork. The match between the laboratory tests and the field measurements appeared to be rather good. The three series of measurements also contributed to a prediction method for wave run-up on dikes.

The spectral evolution of swell propagating across a wide, shallow continental shelf is investigated with extensive data from the North Carolina shelf, on the East coast of the United States. A spectral energy balance equation is proposed for the evolution of swell that includes refraction and shoaling, bottom friction over a movable bed, and Bragg scattering of waves by wavelength-scale bottom topography. This equation is solved numerically using a hybrid Eulerian-Lagrangian model. Hindcasts of swell events during recent field experiments show large variations in wave heights that can be attributed to refraction and bottom friction, and are consistent with a variable bottom roughness. Wave height attenuation up to 73 % (93 % of the wave energy) was observed in moderately energetic conditions. Bragg scattering of waves by wavelength-scale bottom features significantly increases (up to a factor two) the directional spread of waves.

Records of storms in the North Sea are analyzed for evidence that wave groups may be composed of independently propagating components. The Stockwell transform (S-Transform) is used to obtain time-frequency contour plots of wave energy for simulated idealized, interacting wave groups. Additionally, simulated groups with independent directional components, are analyzed using both the S-transform and the Iterative Maximum Likelihood Method to resolve the directions and frequency. Both techniques are applied to the analysis of North Sea storm data obtained from a 3-point array showing that real wave groups can be formed of interacting components that may be propagating in different directions.

Wave transformation on a transect crossing the surf zone of a fine grained, gently sloping barred beach has been further investigated with data from a 3-element coherent bottom-mounted pressure sensor line. In particular, field evidence is given for the formation of secondary waves when a moderate long narrowband swell propagated over two consecutive ridge and runnel system in both breaking and non-breaking conditions. Analysis are mainly done in the frequency domain, including also higher spectral analysis (bicoherence). The observed spatial variation in bicoherence values in the non breaking case is surprisingly low despite the fact that significant wave decoupling occurred after the bar. This implies that the phenomenon of decoupling can not be completely ascribed to the increase in water depth. On the other hand, wave breaking appears to weaken the strength of nonlinear coupling but does not affect (or at least hardly) the energy transfer to higher frequencies.

The wave transformation processes at Starling Creek Marina, Virginia have been studied using a publicly available wave transformation model, RIDE. This model simulates the following major wave transformation processes: refraction, diffraction, reflection, shoaling, energy dissipation caused by bottom friction and wave breaking, and harbor resonance. Simulation of possible wave conditions for the original bathymetry were done first, and the results indicate that waves coming from W to WSW may intrude into this creek and cause damages on piers and difficulty for vessel operation at the marina. In order to protect the marina and nearby docking piers, two alternatives on a breakwater design were proposed. This study indicates that one of the proposed plans is not able to provide sufficient protection. Harbor resonance caused by long period waves should be checked again after the existence of long period waves has been confirmed.

A multi-disciplinary project lead by the U.S. Geological Survey is currently studying the fringing reef off southern Molokai, Hawaii, in an effort to characterize the biological structure and geologic variability of coral reef systems. Wave modeling and field observations were utilized to help understand the physical controls on reef morphology and the distribution of coral species. The morphology of the reef crest, which extends roughly 50 km from east to west and up to 1500 m offshore, appears to be primarily controlled by the amount of wave energy impinging on the coastline. Extratropical cyclones and inter-anticyclonic systems crossing the North Pacific during the winter months generate the wave energy regime that appears to dominate the reef. This North Pacific swell generates near-bed orbital velocities greater than 3.0 m/sec and shear stresses greater than 2.5 N/m² that inhibit substantial coral development in shallow water (<10 m). The reef is sheltered from these waves by the island of Molokai; however, refraction around the east and west ends of the island cause the reef crest to pinch out roughly 5 km from each end of the island. Where the reef crest merges into the shoreline, more robust high-energy corals and low coral cover typify the fore reef. In contrast, more delicate branching corals characterize the central portion of the reef, which is sheltered from the large North Pacific swell, and up to 80% live coral cover.

Wave propagation through an inlet entrance with strong currents and large changes in water level was examined through field measurements and numerical simulations of wave transformation. Extensive field data collection conducted at Grays Harbor, Washington for a 2-month period in 1999 included currents through the water column and directional waves at six locations through the inlet entrance. These data allowed examination of the range of wave conditions that occur, the attenuation of waves through the entrance, and the transformation of waves on a current. One-hundred eighty wave conditions were simulated to represent the entire wave climate and repeated at mean high water, mean low water, with an ebb current, and with a flood current. Thus, the control of water level variation and current on wave transformation through an inlet entrance could be examined quantitatively for a wide range of conditions.

The flow field of a radial neutrally buoyant turbulent jet discharged horizontally into a wavy environment has been investigated. A set of laser induced fluorescence (LIF) measurement was conducted to measure instantaneous surface elevation and jet centerline movement simultaneously. The measurement shows dynamic changes on jet oscillation due to waves motion. The pattern of jet oscillation due to waves was classified into three categories. A simple physical model was proposed to estimate the jet oscillation in the near field.

A spectral wave transformation model with a diffraction term, newly formulated from a parabolic approximation wave model, is proposed and checked against the Sommerfeld solution. It is seen that the present wave model gives reasonable predictions.

The collision of solitary waves in branching channels is investigated on the basis of the extended Boussinesq equations in terms of the velocity potential and the surface elevation. The equations are transformed into a generalized curvilinear coordinate system so that the numerical domain can be fitted to the channel boundaries of a complex geometry. The transformed equations are then solved numerically by using a high-order finite difference method. The merit of the potential formulation is described and it is confirmed that the computational efficiency can be significantly improved compared with a velocity formulation. A series of computations is carried out for two types of branching channels with basic shapes. The general features of the transformation and interaction of solitary waves near the branch are described, and the effects of the channel geometry on the maximum crest height are examined. It is shown that the influence of the channel geometry on wave transformations is significant and that the maximum crest height becomes almost three times as large as the incident wave amplitude in wide channels.

A new method valid for highly dispersive and highly nonlinear water waves is presented. It combines a time-stepping of the exact surface boundary conditions with an approximate series expansion solution to the Laplace equation in the interior domain involving up to fifth-derivative operators. A numerical model is developed in a single horizontal dimension and it is used to study modulational instability in deep water.

In this paper, a curvilinear Boussinesq model is further improved in order to be used in more practical applications. Firstly, the energy dissipation due to wave breaking is considered by introducing an eddy viscosity term into momentum equations. Secondly, the slot technique is introduced into the curvilinear model for simulations of wave run-up/run-down in swash zones. Thirdly, Smagorinsky subgrid lateral turbulent mixing is utilized to account for the effect of the resultant eddy viscosity on the wave-generated underlying flow, in addition, a TMA spectral wave maker is implemented in the model for simulations of irregular waves. Finally, the model is used to simulate wave propagation in Ponce de Leon Inlet. Model/data comparisons show the fully nonlinear Boussinesq model give accurate results for nonlinear wave transformation over irregular bathymetry. It is also shown that the curvilinear model is an efficient model for wave computations in large computational regions with complex geometry.

This paper deals with nonlinear features of some Boussinesq-type equations. Due to the flexibility in deriving a set of Boussinesq-type equations, analysis of the derived set is an important process in determining its performance. Features of three recent Boussinesq-type equations are discussed here. Accuracy of the steady, permanent-form waves admitted by these equations is discussed with respect to the exact equations from `Stream Function' theory on a two-parameter space of wave number (frequency) and wave height. Computed results from three Boussinesq-type models for a practical case of transformation of waves over a submerged bar are presented and discussed with respect to their linear and nonlinear features and experimental measurement.

A fully nonlinear dispersive numerical model based on non-linear mild-slope equations is developed to clarify the characteristics of stem waves in shallow water. Simulation of wave transformation along a wave-absorbing breakwater indicates the occurence of stem waves, with comparison of numerical, analytical, and experimental results showing good agreement.

The authors describe a Petrov-Galerkin finite element method with third-order accuracy for the numerical solution of the 1-term Beji-Nadaoka model for weakly nonlinear dispersive water waves in one dimensional horizontal domains. Finite elements are used in both space and time domains. Dispersion correction and a highly selective dissipation mechanism are introduced through additional streamline upwind in the weighting functions. Linear interpolation in space is retained and coupled with an implicit one-level time integration scheme. An accuracy and stability analysis is presented. The numerical results are compared to experimental data of waves propagating over a bar. It is concluded that the proposed finite element method possesses very good features.

A procedure is presented for the dynamic handling of the boundaries of Boussinesq-type wave models that enables to control the reflection properties. The main purpose of the procedure is the reduction of spurious reflections at open boundaries. The procedure also allows, however, the modeling of partial reflection at closed boundaries. The approach chosen takes into account the effect of wave direction, wave period, and wave height, in order that irregular waves, waves at arbitrary angles, and steep waves can all be handled properly. An innovative aspect of the developed method is that it can equally well be used for strongly dispersive waves, since besides the angle of outgoing waves also the celerity is determined dynamically. The results presented demonstrate the feasibility of the approach; reflection coefficients of only about 1% are obtained for regular waves, varying angle, period, as well as steepness.

A weakly nonlinear mild-slope equation has been derived directly from the continuity equation with the aid of the Galerkin's method. The equation is combined with the momentum equations defined at the mean water level. A single component model has also been obtained in terms of the surface displacement. The linearized form is completely identical with the time-dependent mild-slope equation proposed by Smith and Sprinks. For the verification purposes of the present nonlinear model, the degenerate forms are compared with Airy's non-dispersive nonlinear wave equation, classical Boussinesq equation, and second-order permanent Stokes waves. In this study, the present nonlinear wave equations are discretized by the approximate factorization techniques so that a tridiagonal matrix solver is used for each direction. Through the comparison with physical experiments, nonlinear wave model capacity was examined and the overall agreement was obtained.

Boussinesq-type equations with second order dispersion axe derived for an arbitrary distribution of vorticity. The governing equations have the velocity at an arbitrary depth as a dependent variable and terms involving vorticity are kept as integrals. Linear dispersive properties are shown to be accurate to the order of dispersion when compared to the exact solution. Current input conditions (from a large scale hydrodynamic model) and the scheme for the numerical model are obtained in order to later test model results against measurements from an experiment in a wave flume for the case of waves propagating against a vertically sheared current.

A new breaking formulation for deterministic evolution equations in the frequency domain is developed. In contrast to conventional breaking formulations based on a bulk energy dissipation model, the new model is based on the surface roller model, which is known to model breaking well in time domain Boussinesq formulations. The toggling between the frequency and time domain is performed using Fast Fourier Transform. Fast Fourier Transform is furthermore used for reducing the computational work in each spatial point from O(N²) to O(N log N), N being the number of frequency components. Initial results for the spilling breaker test of Ting and Kirby show that the new model is able to describe wave height decay satisfactorily. Due to the equivalence with the time domain breaking formulation, an improvement in wave shape was expected when comparing to traditional breaking models in the frequency domain. Surprisingly, this improvement is only marginal at present.

In this paper we describe a numerical algorithm which deduces characteristics of the bottom bathymetry given free surface elevation records dense in space but sparse in time. The method makes use of the Levenberg-Marquardt numerical optimization scheme in conjunction with a time-domain nonlinear model. Iteration occurs until the mismatch between the free surfaces of the data and model are minimized; the bathymetry is adjusted in order to achieve this minimum. The sensitivity measure is a by-product of the calculation, and determines the invertibility of the system. Due to convergence concerns, we limit ourselves to deduction of bathymetric profile parameters. Tests of the system using monochromatic, irregular and groupy waves show favorable results; the latter is particularly notable given the difficulty standard inversion methods have had with groupy waves. A two-stage system is also outlined, in which a simple parameterization for a nearshore bar is developed and utilized. The first stage determines the mean profile, while the second stage determines the bar characteristics using the first stage results as the initial iterate. To extend the method's capabilities further, the use of phase speed records is discussed.

An overview of global wave modeling methods currently used by the U.S. Navy is presented, and the advantages and disadvantages of various approaches are discussed. Two Pacific Basin swell events are presented for illustration, one typical of winter events at the California coast, the other typical of summer swells. The WAM model performs poorly in both cases. Model underprediction of wave generation is the primary source of error for the winter swell, while wave propagation errors explain the poor performance for the summer swell. A new approach for reducing error associated with propagation is proposed. Test results for a canonical case are discussed.

The evaluation of design waves for coastal protection structures in Wadden Sea areas can be improved essentially by applying advanced mathematical wave models like the third-generation SWAN. Nevertheless the analysis of directional spectra in shallow environment shoes the demand for further development in areas with complex morphology.

Several models based on the finite volume method are developed for simulating weakly nonlinear, dispersive waves in intermediate and shallow water. All models are at least second-order accurate in space and time and differ mainly in the data reconstruction at cell boundaries. The different reconstruction techniques include traditional linear averaging, Total Variation Diminishing (TVD), and Essentially Non-Oscillatory (ENO) methods. All models use Roe's approximate Riemann solver to compute fluxes. Model predictions are compared with analytical solutions, numerical predictions obtained with a second-order accurate finite difference model, as well as experimental data.

Wave spectra pattern is important information for the input in hydraulics experiments and design of offshore structures. The purpose of this study is to investigate the wave spectral model specifically applicable for typhoon-generated waves. For this, analysis of wave spectra is carried out on measured data obtained by COMC data buoys. This study found that the spectral parameters were related to typhoon states. The typhoon wave spectral model based on JONSWAP formulation but as a function of distance and intensity for the specific track in this study was outlined.

This paper presents the development of a parametric model linking the free-surface elevations with the orbital velocities field under an irregular wave. The system identification procedures are applied to estimate the parameters of the model based on data recorded in the wave tank. The free-surface time series are taken as input data and the output data are components of the particle velocity vector. A linear time-invariant model with the static nonlinearities at the input side incorporated is assumed. In the study different system identification procedures are applied for two cases—firstly when orbital velocities are modelled at points that are always submerged in the water and, secondly, in the surface zone where measurement points are not continuously submerged. This paper demonstrates the results of modelling the horizontal component of the orbital velocity in comparison with wave kinematics data taken in a wave flume using Laser Doppler Velocimetry specifically designed to give accurate measurements also in the vicinity of the mean water level. Comparison between the modelled and observed velocity time series presents a sufficiently good agreement to prove the effectiveness of the applied approach. The SI techniques applied to determine from the free-surface records the orbital velocities as well as other hydrodynamic parameters such as particle acceleration and forces may be very important and useful in engineering and oceanography.

The Figueira da Foz harbour is located at the mouth of the Mondego River in the West coast of Portugal. Two shore-connected breakwaters that, due to their layout, have a quite poor performance shelter it. In fact, some of the incident waves cause large movements in the ships moored at the general cargo quay. The breakage of mooring lines is a quite common accident there. This paper presents the methodology employed and summarizes the results obtained in both the wave penetration study when the harbour basin is dredged up to –7.00 m C.D. and the study of the wave effects on the behaviour of a ship moored at the general cargo quay.

In situ visual observations concerning the entrainment of air bubbles after wave breaking were carried out (Kojohama, Ohkishi and Furubira coasts in Japan). This paper presents a discussion of the behavior of air bubbles under breaking waves as well as the effects of these bubbles on the fluid and sediment based on the results of the observations. Typical bubble cloud structures are identified and classified according to the breaker type. Furthermore, the major differences between the three-dimensional eddy structures containing an obliquely descending eddy (ODE) found in the surf zone relative to those in experiments were investigated by tracking the bubbles involved in the vortices.

This paper presents the results from an experimental work to characterize the underwater sound field radiated by breaking waves. Measurements of the ambient noise in the frequency range 20Hz – 20kHz, generated by laboratory breaking waves, are presented. It has been observed that the sources of sound in spilling breakers are primarily in the frequencies ranging from 300 Hz to 20 kHz. The plunging waves, however contributes to the noise spectrum from less than a few hundred hertz to 20 kHz. Attempts have been made to correlate breaking wave acoustics with the dynamics of breaking waves. The acoustic radiated energy has been found to be proportional to energy dissipation and the square of the maximum wave slope parameter.

A spilling breaker model is implemented in a two-dimensional fully nonlinear coastal wave propagation model. A maximum surface slope breaking criterion is used to identify breaking waves within the incident wave train. Energy dissipation is achieved by specifying an absorbing surface pressure over breaking wave crest areas. The pressure is proportional to the normal particle velocity on the free surface. The instantaneous power dissipated in each breaking wave is specified proportional to the dissipation in a hydraulic jump of identical characteristics. Computations for a periodic wave shoaling and breaking over a plane slope are compared to laboratory experiments. The agreement is quite good, although more work remains to be done in refining the breaker model parameters.

Spectral wave breaking parameterizations are evaluated using 15 days of field measurements from the Duck94 study at the FRF. Measurements include 14 pressure gauges from 8-m depth to the shoreline and 120 wave events (wave heights of 0.5 to 4 m and periods of 4 to 16 s). The Battjes and Janssen model applied with a full Rayleigh distribution to calculate the percentage of wave breaking gave the smallest errors. Bore-type models like Battjes and Janssen degrade significantly as grid spacing increases (resolution greater than 15 m for the FRF comparisons). For applications with coarser resolution, a limit must be placed on dissipation or a simpler breaker model should be applied. Use of spectral transformation models in the surf zone can reduce RMS error by more than a factor of three compared to a monochromatic model defining breaker height as 0.78 times depth. Including the Battjes and Janssen breaking relationship in a monochromatic model reduces error by a factor of two. Spectral breaking models accurately represent wave height in the surf zone, but do not reproduce changes in spectral shape for multi-peaked incident spectra.

This study presents the discovery of a new type of wave breaking over a submerged breakwater. Our findings were made through laboratory experiments. In this new type, wave breaking first occurs at a wave's front part, not at the top of the wave crest. Next, the wave crest passes over the breakwater's crown without breaking. In this study, we call this wave breaker a wave front breaker, and the process of wave transformation and the conditions for the wave front breaker to occur are clarified. The wave kinematics of the wave front breaker is also investigated by PIV and LDV measurements. Consequently, it is shown that the occurrence of the wave front breaker strongly depends on the incident wave length, and the wave transmission coefficients of the wave front breaker become larger. It is also found that an inverse layer of the mass transport velocity exists near the seabed against the main region of the mass transport velocity. Furthermore, the direction of the mass transport velocity near the toe in the inverse layer is onshore, while that of the maximum acceleration is offshore and the value of the acceleration increases as the measuring points get closer to the seabed and away from the toe.

The study investigates the effects of reflective seawalls on wave breaking processes and mean flow distribution throughout the surf zone. The presence of reflective structures results in a significant change of wave breaking characteristics and turbulence structure in the surf zone. The organized large vortexes, which cause onshoreward mass transport, will also be changed thus changing the undertow considerably. The physical processes and mechanisms of wave breaking and turbulence structures in presence of a seawall have been investigated using visualization techniques. A model for evaluating the distribution of undertow in front of a reflective structure is also proposed on the basis of the change in wave fields due to the presence of reflected waves in the surf zone. The model is in reasonable agreement with the experimental results. It has been found that the presence of reflected waves due to reflective condition in the surf zone changes the wave breaking characteristics and reduces the magnitude of undertow. The results of the present work can be implemented for predicting cross-shore sediment transport models and beach evaluation models where reflective conditions exist.

Water surface elevations and fluid velocities were measured in a laboratory surf zone created by the breaking of narrow-band waves on a 1/35 plane slope. The incident waves formed wave groups that were strongly modulated. The wave characteristics inside the surf zone were influenced by low-frequency waves. The waves with the smaller initial heights break closer to shore and have higher wave-height-to-water-depth ratios at breaking than the waves with the larger initial heights. When normalized by the period-averaged water depth, the wave height has a narrow variation in the inner surf zone. The standard deviation of the wave period increases as the water depth decreases due to the effects of long-wave motion. Turbulent kinetic energy and Reynolds stress were estimated at two different levels under the wave trough level by ensemble averaging. The distributions of the period-averaged turbulent kinetic energy and Reynolds stress for narrow-band and broad-band waves are different in the outer surf zone, but similar in the inner surf zone. It is suggested that the wave and turbulence characteristics in an irregular wave surf zone are determined by the breaker types, which in turn, are determined by the wave height and wave period distributions of the incident waves, and the beach slope.

Artificial reefs are increasingly used as an active shore protection measure. Nevertheless, the physical processes occuring at these structures are still not fully understood. Existing design formulae usally take into account only the change in wave height over the reef, i.e. the energy transfer within the wave spectrum is not considered. Physical model tests on artificial reefs have been performed at Leichtweiβ-Institute for Hydraulic Engineering, focussing on the energy transfer and on local effects occuring at the reef. First results are discussed in this paper.

We present an accurate three-dimensional (3D) Numerical Wave Tank (NWT) solving the full equations in the potential flow formulation. The NWT is able to simulate wave propagation up to overturning over an arbitrary bottom topography. The model is based on a high-order 3D Boundary Element Method (BEM) with the Mixed Eulerian-Lagrangian (MEL) approach. The spatial discretization is third-order and ensures continuity of the inter-element slopes. Waves can be generated in the tank by wavemakers or they can be directly specified on the free surface. A node regridding can be applied at any time step over selected areas of the free surface. Results are presented for the computation of overturning waves over a ridge and their kinematics.

Smoothed Particle Hydrodynamics (SPH) methods have recently been used to examine water wave motions. Here we apply SPH to the problem of water waves impinging on a deck of an offshore platform. Laboratory experiments by Cox and Ortega are used to motivate the numerical modeling efforts. Realistic comparisons are found, although no direct one-one comparisons are made as the resolution of the numerical model was insufficient at that time.

A 2D fully nonlinear NWT is developed based on the potential theory, mixed Eulerian-Lagrangian (MEL) time marching scheme, and boundary element method (BEM). Wave profiles and wave kinematics of highly nonlinear waves are calculated using the NWT and the results are compared with linear, Stokes second-order theory and experimental values. It is confirmed that the spatial variation of intermediate-depth waves along the direction of wave propagation is caused by the unintended generation of second-order free waves, which was originally investigated both experimentally and theoretically (3^rd order perturbation theory) by Goda. The various phenomena observed by Goda are clearly reproduced by the present fully nonlinear NWT. It is shown that the wave kinematics above mean water level can be significantly different from the perturbation-based prediction. It is also found that small mean positive or negative flows can be generated below mean water level depending on the water depth and wave condition.

Wave frequency focusing has been used in two-dimensional (2D) laboratory wave tanks to simulate very large waves at sea, by producing large energy concentration at one point of space and time. Here, three-dimensional (3D) frequency/directonal energy focusing is simulated in a fully nonlinear wave model (Numerical Wave Tank; NWT), and shown to produce very large waves. This method alone, however, cannot explain why and how large waves occur in nature. Self-focusing, i.e., the slow growth of 3D disturbances in an initially regular wave train, is shown to also play a major role in the formation of "freak waves". Self-focusing is studied in a more efficient space-periodic nonlinear model, in which long term wave propagation can be simulated. The combination of directional/frequency focusing and self-focusing, and resulting characteristics of large waves produced, could be studied within the same NWT.

This paper reports results of numerical wave flume predictions against experimental data for violent overtopping. The numerical scheme solves the non-linear shallow water equations which, for violent overtopping should not be valid as they neglect vertical accelerations. The results presented show relatively good agreement with experimental results under certain conditions. The paper reviews and identifies the conditions under which engineers can use the numerical model as a viable design tool.

In this study, three-dimensional fluid motion in waves around the head of a semi-infinite vertical breakwater was investigated using large-eddy simulation (LES). Wave deformation, separation, and evolution of vortices were investigated to obtain basic data in order to develop a reliable model for predicting local scouring and for estimating local fluid forces acting on the structure. Moreover, the processes by which separated eddies are generated and evolved were discussed in detail in order to determine the mechanisms by which the separated vortices cause local failures of armor blocks and the mound of a breakwater. Two significant vertical separations appeared around both edges of the breakwater head, especially when the wave front passed each edge. The velocity field around the head of the breakwater became significantly three-dimensional because secondary horizontal and helical eddies arose due to the vertical gradient of shear associated with the vertical separation. Furthermore, during interactions among these eddies, a complex three-dimensional eddy structure was formed around the head of the breakwater. It is possible that the vertical velocity caused by the three-dimensional eddy structure is associated with the suspension of sediment around the structure.

Submerged breakwaters are a possible solution for the prevention of coastal erosion problems. They guarantee increased protection between themselves and the coastline, diminishing the risk of coastline erosion and assisting sand accretion or retention. Their efficiency depends and it's normally evaluated through the knowledge of the incident, transmitted and reflected wave heights. A different approach of the problem can be done through the measurement of incident, reflected and transmitted wave energies using a full energy concept, i.e., through the measurement of the velocity flow field and sea surface elevation for a regular wavelength. The results presented show the variation of the measured kinetic, potential, total and turbulent kinetic energies, as a function of the distance to the submerged breakwater, calculated through the phase-dependant measured velocity profiles and water surface elevation. Laser Doppler anemometry technique was used for measuring flow velocities and experiments were carried out at the wave tank of the Hydraulics Laboratory of the University of Porto's Faculty of Engineering.

Wind waves may be amplified in many Great Lakes harbors due to reflection and resonance phenomena. Although the short period waves do not excite the harbors at their fundamental periods, wave amplification in many situations has been sufficient to pose navigational concerns. It is useful to dissipate a portion of the wave energy in order to reduce wave heights to acceptable levels. We have performed numerous laboratory studies at the University of Michigan Hydraulics Laboratory utilizing stone to provide energy dissipation in order to reduce wave activity to an acceptable level. These studies have considered a wide array of stone size and use from large armor stone that would be statically stable under design waves down to much smaller stone confined within gabions. It is likely that a significant portion of this energy dissipation occurs due to fluid motion in the pore spaces. We have systematically varied the stone size in laboratory models for both enclosed harbors and jettied harbor channel entrances. These experiments have indicated that the reduction in wave amplitudes is independent of the stone size. It is therefore concluded that the results of the small-scale laboratory model tests may be applied to estimate prototype harbor behavior for typical Great Lake harbor settings. General results of these studies are discussed with respect to the general effectiveness of different configurations for reducing wave amplitudes.

The paper will present the experimental set up and description of the spatial evolution of waves propagating in the swash zone. Wave and velocity measurements performed in the LIM laboratory of the UPC University are described. Velocity profiles are acquired with a Doppler Velocimeter Profiler, which enables simultaneous high frequency velocity profiles measurements over the whole swash zone. Advantages of this new technique with respect to more traditional ones are presented. Velocity profiles are used to estimate bed shear stresses in the swash and to estimate the friction factors.

This paper reports the experimental Project "SPANWAVE-SPPORITA" carried out at the "Canal de Investigación y Experimentación Maritima" of the Polytechnic University of Catalonia (Barcelona, Spain). The Project goals were to obtain detailed and accurate measurements of turbulent and mean velocities over the bar and trough regions, for regular and random waves breaking over the bar. Four wave conditions were simulated, and both surface elevation and velocity measurements were carried out at a large number of locations. The experiments are considered successful and provide a unique data set on surfzone hydrodynamics over a barred beach. Preliminary data results reveal quite interesting aspects, deserving further investigation.

The design and construction of a small wave-sediment tank, built and instrumented for under $10,000, is described. The tank is equipped with a piston-type wavemaker, capable of producing both small-amplitude and solitary waves. The middle section of the tank contains a sediment bed appropriate for wave-soil-structure interaction and sediment transport experiments. Wave energy is absorbed by a gravel beach located at the opposite end of the tank from the wavemaker. Instrumentation includes three capacitive wave height gauges. The wavemaker is controlled by a desktop computer, which also provides data-logging capability. Applications of this wave-sediment tank to research into grounded ship migration and barge added-mass are presented.

A second-order wave generation algorithm called "Delft-Auke/generate" which includes online Active Reflection Compensation is presented. Results are shown from various experimental and numerical verification tests which confirm the software is capable of generating very accurate regular and irregular waves. The short-wave ARC performance tests show that the reflection coefficient (in terms of wave height) is in the order of 5% which is much less than can be achieved for "conventional" long wave ARC.

The theory of 2D and 3D active wave absorption is outlined in Fourier space and the principles of approximate time-space realisation are given. An analysis method by which the system checks its own performance is derived and the usage is demonstrated for a wave flume case. For active absorption of oblique waves a qualitative test shows promising results.

For MARIN's new Offshore Basin, an L-shaped segmented wave generator has been developed and installed that allows high and multidirectional deepwater waves while simultaneously allowing layered surface current in one direction. Other features are a low profile above water, very accurate drive and control system, second-order wave steering, selectable wave groupiness, and active absorption of reflected waves. The system can produce a new wave field accurately from scratch with only one single correction.

Experiments to measure waves, currents, and sediment transport rate for two breaker types, plunging and spilling, were conducted in a large-scale three-dimensional physical model. A large difference in cross-shore distribution and total sediment transport rate was found between the two breaker types. Existing predictive equations for total transport rate did not predict the data well. With the exception of the Kamphuis equation, which included a dependence on wave period, the predictive equations did not differentiate between breaker types. Sediment transport increased where dissipation was high for plunging waves, but high dissipation did not necessarily produce increased transport rates with spilling waves.

Two cases of scaling waves at tidal inlets with physical models are examined. One case was for a study of wave breaking over an ebb shoal in the presence of ebb currents (1:50 scale). Wave heights were compared for two different model scales. The other case compared physical model and prototype currents adjacent to a jetty resulting from a combination of tidal and wave-generated currents using a 1:75 scale model. Results indicated tidal inlet models at these scales reproduce the nearshore wave heights and currents well.

A series of laboratory experiments was conducted to understand the kinematics and dynamics of short crested breaking waves. The simulation of wave breaking was achieved through wave-wave interactions of a frequency and amplitude modulated wave packet. Directionality and short crestedness were added to the breaking wave packet by varying the amplitude distribution of the wave paddles. The experiments have highlighted the basic features of a short-crested breaker through a series of still and movie pictures. Surface elevations at prescribed locations within the breaking wave field were monitored using wave gauges. Flow visualizations, incorporating digital imaging illuminated by a laser light sheet, were used to elucidate the mixing process.

Large-scale experiments of breaking wave attack on slender cylinders were performed in the LARGE WAVE CHANNEL at the Coastal Research Centre in Hannover, Germany. Using large-scale physical models the influence of scale effects on the real physical mechanisms can be widely minimized. Very steep waves (similar to "freak waves") were generated to investigate extreme breaking wave impacts.

The purpose of this study is to develop a quasi-3D numerical model that is applicable to nearshore currents over barred beaches. The presented model is composed of two sub-modules of wave field and nearshore current field. The wave filed was determined using wave by wave approach to consider the irregularity of waves. The current field was determined from the Q-3D model, taking account of the effects of wave decay and recovery processes in the surf zone. The present Q-3D model was calibrated and verified by comparing with data measured over barred beaches in the field. The applicability of the Q-3D model was discussed.

The action of large waves causes the disappearance of vortex ripple flow and produces sheet flow, although numerous experimental studies have not clarified why this occurs. The shape of a vortex ripple indicates that the flow velocity over the crest of the ripple is higher than the velocity over the trough, with the resultant flow field inducing low pressure above the crest of the ripple such that upward seepage inside ripples will occur. An oscillating water tunnel and numerical simulations were accordingly employed to elucidate the phenomenon; ultimately showing that the oscillatory flow-produced excess pore pressure due to low pressure around the ripple crest is larger than the overburden soil pressure such that ripple fluidization occurs. The effect of wave height, permeability of sand, and ripple shape are also investigated using numerical simulations.

This small scale laboratory study deals with the action of monochromatic or bichromatic waves on a sand bed of initial constant slope. The aim was to address the effects of nonlinear wave-wave interactions onto bed evolution and bar formation. Properties of a spurious wave, produced either by the wavemaker or by rapidly varying bathymetry, were used to obtain or not nonlinear interactions. A strong relation between the wave envelope and the bathymetric profile was found in the breaking case as in non-breaking wave conditions.

This paper presents a detailed study on the sensitivity of a number of important wave and current parameters (wave height, driving forces, wave-induced current) to the directional and frequency spreading of the random sea. The analysis is carried out using a purpose-built wave and current model. Three forms of input are used, a directional spectrum, a frequency spectrum and a monochromatic wave, corresponding to different sea conditions, short-crested, unidirectional and monochromatic waves. It is concluded that the directional spreading affects radically the wave and current fields. Its effect is much more pronounced on the driving forces and longshore current velocity (differences up to 50%) rather than on the wave heights. Moreover, the obtained results show that the above quantities are not very sensitive to the frequency spreading.

The commonly used Bailard sediment transport model relates sediment suspension to the fourth velocity moment. However field studies have shown that wave orbital acceleration, which is related to vertical wave asymmetry, is also important for sediment suspension. The general view is that asymmetry is unrelated to velocity moments. Here, incident wave cross-shore velocity data from dissipative beaches shows very similar cross-shore distributions for both vertical wave asymmetry and kurtosis. The implications for sediment transport of this possible relationship are investigated by obtaining the cross-spectra between sediment suspension and (i) a Bailard-type pick up function (u⁴)^3/4, and (ii) vertical asymmetry, as the Hilbert transform of the incident cross-shore velocity. For dissipative conditions, both the Bailard term and asymmetry represent similarly sediment suspension. For reflective conditions the Bailard term fails to describe suspension whilst vertical asymmetry is very strongly correlated to sediment suspension. Accurate representation of sediment suspension in models should include the effects of vertical asymmetry.

Construction of beach nourishment projects requires large volumes of sediment, which are usually obtained by the removal from borrow pits located in reasonably shallow water. These modifications of the nearshore bathymetry have the potential to affect wave transformation processes and thus to alter the equilibrium shoreline planforms landward of the borrow pits. Recent cases of erosional hot spots (EHS's) associated with beach nourishment projects have increased interest in the prediction of the mechanisms of borrow pit alteration of the local wave field. A better understanding of the interaction of borrow pit characteristics such as size and depth with the incident wave field is needed to determine the effect of the pits on the nourished beach and to anticipate the effects of various designs. The present study employs numerical and theoretical approaches. The numerical analysis uses a boundary element approach for a pit of finite dimensions in a uniform shallow water depth as in Williams. An analytical solution to the shallow water pit problem is obtained using the general method of MacCamy and Fuchs with a circular pit instead of a solid cylinder and allowing a solution inside the pit with appropriate boundary conditions. For both the numerical and analytical solutions, the velocity potential can be determined anywhere in a fluid domain containing a pit, or a shoal, of uniform depth. This allows for the calculation of the free surface elevation as well as other wave related quantities such as wave direction, wave energy flux and wave-induced shoreline change.

Several stretches of shoreline in the Red River Delta, Vietnam, are suffering from severe erosion, especially an area in the southern part of the delta known as Hai Hau Beach. Commonly found explanations for this erosion is the construction of a large dam upstream the Red River Delta and the closing of a river branch that used to supply sediment to the beach. However, in this study it is shown that the prevailing wave climate during the winter monsoon in combination with the complex topography of the delta create longshore transport gradients that promotes erosion at Hai Hau Beach. A newly developed two-dimensional random wave transformation model based on the mild slope equations was employed for a 20-year long time series of hindcast waves to compute representative nearshore wave properties for the Red River Delta shoreline. These properties were utilized to compute the longshore sediment transport rate along the delta from which shoreline evolution was inferred.

Interest has developed to use borrow material from resource areas located on the inner continental shelf offshore New Jersey for beach replenishment purposes. A study was conducted to quantify the potential impacts of the offshore dredging and consequent beach nourishment on the local sediment transport patterns. In order to determine the offshore sediment transport patterns at the borrow locations, sediment transport rates were determined by coupling the results of spectral wave modeling with ambient current measurements. Having determined the sediment transport rates and directions at the borrow locations, and by knowing the volume of sediment to be mined, estimates of the borrow location recovery time were determined. These recovery time estimates were utilized to determine the time scale of influence on wave transformation, nearshore sediment transport, and re-mining frequencies.

The impact of inter-model coupling on regional scale numerical predictions of wind-waves, marine circulation, and sediment transport is investigated. This is done using the COupled MArine Prediction System (COMAPS), which consists of parallel-processing versions of the CH3D-SED circulation and sediment transport model, the WAM wind-wave model, and the WCBL bottom boundary layer model. COMAPS includes physics couplings between wave and current motions at the water surface and wave, current, and sediment motions at the marine bed. Adriatic Sea hindcasts are discussed. These indicate that the coupling mechanisms have significant impacts on coastal water levels, currents, and wave heights, as well as basin-wide sediment transport.

The time-dependent cross-shore sediment transport model CBREAK is compared with the irregular wave experiment on dune profile evolution due to overwash. CBREAK includes sediment suspension by turbulence generated by irregular breaking waves and bottom friction. CBREAK with the bottom friction factor calibrated to reproduce the measured wave overtopping rate is used to predict the irregular wave breaking and overtopping of a dune as well as the sediment suspension and net onshore sediment transport on the overwashed dune. The computed results are qualitatively realistic but CBRAEK in its present form can not predict fairly uniform erosion on the seaward face of the dune.

A new sediment transport model is proposed, which uses linear wave parameters (e.g. wave height H, and period T) to predict wave-induced net bedload transport in a given water depth h, and for given seabed properties and a given seafloor grain-size distribution. Steady-state streaming and net differential shear stress on the bed yields a shear-induced sediment transport in the direction of wave propagation (i.e. onshore). On the other hand, pressure-induced dilatation effect will force sediment transport opposite to wave propagation (i.e. offshore). The net wave-induced sediment transport is the superposition of these shear and pressure effects. It is shown that under large (winter) waves, pressure effect dominates — resulting in a net offshore transport near the shore (e.g. sediment erosion from the beach region), and under mild (summer) waves, shear effects dominate — resulting in a net onshore transport near the shore (e.g. sediment accretion into the beach region).

Because both contaminant and nutrient cycles in the Laurentian Great Lakes depend on particle behavior and movement, sediment transport is a critical component of many of the water quality models being developed to understand and manage this important resource. To avoid complicated models that cannot be supported by the available field data, we have used observation-based, empirical analysis as the basis for developing methods of predicting sediment resuspension from relatively simple measurements of the surface wave field. Our modeling is based on data obtained from instrumented tripods designed to measure near-bottom hydrodynamic and sedimentological conditions for extended periods of time. Because of the long duration of the deployments, it usually is impractical to both sample and record the data at the high frequency that would be needed to resolve the effects of individual surface waves. Instead, we have used a system of burst sampling, in which we sample the sensors at high frequency during a period of time that is repeated at an interval appropriate for the deployment duration. Rather than record the individual samples during the burst, we record only statistics obtained from the individual samples. Our results show that simple representations of the surface wave field obtained from the burst statistics can be used to model sediment transport in wave-dominated environments. We also show that once the model parameters are determined, the forcing wave conditions can be derived from other sources, including wind-driven wave models, with comparable success.

The time-averaged, depth-integrated suspended sediment model based on the sediment suspension and settling rates is combined with the nonlinear time-averaged irregular wave model CSHORE. In this sediment model, the suspension rate is proportional to the wave energy dissipation rate per unit volume of water. Beach profile evolution tests were conducted to calibrate CSHORE and estimate the suspension rates which were found to be much larger than the rates of the bottom elevation change. Equilibrium profile tests were also conducted to verify CSHORE for its capability in predicting the cross-shore variations of the statistics of the free surface elevation and cross-shore velocity from outside the surf zone to the inner surf zone. The sediment model combined with the calibrated CSHORE is shown to be capable at least qualitatively of predicting the cross-shore variation of the measured suspended sediment concentration above the equilibrium profile.

A dilute sediment transport model based on the two-phase mass and momentum equations is introduced with appropriate closures on the fluid turbulence. Due to the presence of the sediment phase, an important damping mechanism in the fluid turbulent kinetic energy equation is derived and modeled. The proposed model is solve both analytically and numerically to study the sediment transport experiment in a steady uniform open channel flow. In the analytical approach, we made additional approximations in order to obtain simple solutions. The analytical solution show clear improvement, which is due to a better modeling on the additional damping mechanism in the fluid turbulent kinetic energy equation, on the calculated concentration profile as compare with the solutions from the Rouse formula. A numerical model, which solves the complete dilute two-phase equations, is also developed. The accuracy of the numerical is checked with the experimental data. With an appropriate closure on the particle stress, the numerical model can be extended to solve the sheet-flow problems in the future.

The time-dependent evolution of rip currents is investigated in this paper using a numerical model based on Boussinesq-type equations. A numerical wave basin was set up to reproduce the laboratory experiments of Haller et al.. The bathymetry consists of a barred beach with two rip channels. Waves propagating over the bar break on the bar while those propagating through the gap break closer to the shoreline. This sets up a spatial variation of the wave-induced excess momentum flux and drives a time-varying circulation pattern. Large-scale horizontal eddies are also generated at the edges of the rip channels and advected offshore. Time histories of the measured velocities have been compared with the Boussinesq model predictions. The numerical model reproduces the overall trend in the unsteady behavior of the rip current but pronounced differences are observed in the flow exiting the rip channel.

The paper analyzes how prescribed errors in the boundary conditions along both upstream and downstream cross-shore boundaries spread inside the computational domain. For simplicity we consider a longshore uniform plane beach with monochromatic, obliquely incident waves. It is found that the mismatch at the upstream cross-shore boundary tends to propagate away from the surf zone as if choosing a least-resistance path while the influence of the errors in the downstream boundary condition is limited to the adjacent area of the downstream boundary. Both the numerical and analytical solutions show that errors in the longshore current specified at the upstream boundary exponentially decay in the surf zone at a rate proportional to the bottom friction. In the case of excessive flux given at the cross-shore boundaries, a circulation cell tends to develop in the offshore region where the errors caused by the boundary mismatch increase with the cross-shore width of the model domain.

This paper analyzes the waves and currents on beaches with rhythmic or crescentic bars. The goal is to determine under what conditions does the flow in the trough between the bar and shore show similarities with the flow patterns observed on accretional beaches. The nearshore circulation numerical model system SHORECIRC is used for this study. The crescentic shape of the bars is found to refract the waves toward the wide section of the bars driving currents toward the narrow sections of the bar generating rip currents. Channels formed on the narrow parts of the bar reinforce the rip currents within these channels. It is found that waves with an incident angle create stronger flows in the trough. In addition, larger depths over the bar are also found to generate stronger flow in the trough. The flow patterns are seen to be insensitive to the wave height and period for the particular conditions studied.

Experiments have been performed in a laboratory wave basin investigating the effect of wave groups on rip currents. Results show a strong group signature in velocity time series measured in the rip neck. In some cases, mean quantities are also significantly affected. Velocity fluctuations with periods greater than the group period do not appear to be affected by the group forcing. Fundamental differences are found between flow at startup and at later times. These startup transients are extremely high, and the differences from later flow are hypothesised to be because wave-current interaction is not significant in the initial stages of flow development, and because large-scale circulation patterns have not yet developed.

Some of the models already available to identify the onset of general motion of sediment under wave action are considered and a new one is proposed. A laboratory investigation to analyse the phenomenon under observation is carried out by assuming a criterion related to the formation of ripples in their initial stage. The above investigation is referred to regular waves and to monogranular sand bottoms in different initial conditions synthetically described by proper geotechnical parameters. The experimental results are interpreted using the mentioned analytical models, which in any case, do not take into account the initial conditions of sediment.

To study beach morphological change, applicability of remote sensed images has been investigated. Shoreline displacements analyzed by satellite imageries were comparing with field survey data in the corresponding period. The agreements are found to be satisfactory, thus the present analysis using satellite imageries are validated. Next, short term beach evolutions induced by typhoon attack are discussed. Although the analyzed shoreline displacements do not directly correspond to typhoon induced shoreline change, most of the obtained characteristics are found to be physically reasonable. Also, the succeeding shoreline change suggests that beach recovery process occurs after the typhoon-induced erosion. Furthermore, to explain the physical process of the typhoon induced shoreline change, numerical analyses on the wave hindcasting and wave transformation have been conducted. The results of typhoon hindcasting and shallow water transformation reveal that even a small change in wave incident angle results in a great difference in the wave height distributions in the alongshore direction of the study site. This implies that temporal change of wave angle associated with the typhoon-passing is an important factor on beach deformation.

This study deals with the modeling of the 2nd order low frequency directional wave spectrum. The product of Bretschneider-Mitsuyasu frequency spectrum and Mitsuyasu directional function is used for the standard 1st order directional wave spectrum. The 2nd order spectrum is calculated by the convolution developed by Kimura. The sea state parameters (H_1/3)₀, T_1/3 and S_max in the 1st order spectrum are selected so that they satisfy the average relation shown by Goda et al. The frequency spectrum and the directional function of the 2nd order low frequency waves are almost independent. The frequency spectrum and directional function are approximated by simple equations individually. The results show good agreements with the theoretical values.

Study of 3D shear waves has been carried out utilizing the quasi-3D nearshore circulation model SHORECIRC. The emphasis of this study is to investigate the effect of the 3D lateral mixing has on the shear waves, and vice-versa. The kinetic energy equation for the mean flow and for the shear waves has been derived. The momentum and energy balance have been discussed using the numerical results from idealized Duck bathemetry and the wave condition on Oct. 16, 1994. The effect of the 3D dispersion due to the depth varying current on shear waves has been illustrated.

This paper presents an analysis of applying continuous wavelet transform spectrum analysis to the results of laboratory measurement of landslide-generated impulse waves. As the measured results are understandably unsteady, nonlinear, and non-stationary, the application of time-localized wavelet transform analysis is shown to be a suitable as well as useful approach. The analysis on correlating the time-frequency wavelet spectrum configurations in connection with the ambient parameters that drive the impulse wave process, with respect to time and space, leads to interesting and stimulating insights not previously known.

To investigate the run-up heights of nearshore tsunami on the lee side of a circular island, a model has been developed on quadtree grids. The model is based on the Liu et al. using the shallow water equations. The result has been validated experimentally and numerically. The good agreement has been achieved. It should be noted that the run-up heights are mostly dependent on the crest length of incident waves when the crest length is less than the base diameter of the island but are almost insensitive if the crest length is greater than twice the base diameter.

Tsunami generation by underwater landslides is simulated in a three-dimensional (3D) Numerical Wave Tank (NWT) solving fully nonlinear potential flow equations. The solution is based on a higher-order Boundary Element Method (BEM). New features are added to the NWT to model underwater landslide geometry and motion and specify corresponding boundary conditions in the BEM model. A snake absorbing piston boundary condition is implemented on the onshore and offshore boundaries. Results compare well with recent laboratory experiments. Sensitivity analyses of numerical results to the width and length of the discretized domain are conducted, to determine optimal numerical parameters. The (3D) effect of landslide width on tsunami generated is then estimated. Results show that the 2D approximation is applicable when the ratio of landslide width over length is greater than three.

Three benchmark cases are proposed to study tsunamis generated by underwater landslides. Two distinct numerical models are applied to each benchmark case. Each model involves distinct center of mass motions and rates of landslide deformation. Computed tsunami amplitudes agree reasonably well for both models, although there are differences that remain to be explained. One of the benchmark cases is compared to laboratory experiments. The agreement is quite good with the models. Other researchers are encouraged to employ these benchmark cases in future experimental or numerical work.

A dispersion-correction finite difference numerical scheme is employed to simulate the propagation of distant tsunamis over slowly varying topography with improved dispersion effect of waves. The scheme solves the shallow-water equations on a uniform grid system. However, the actual computation is made on an imaginary grid system whose grid size is adjustable according to the condition required to satisfy local dispersion relationships. The present model is applied to the simulation of a historical tsunami event. Numerical results are compared with the tide gage records, and reasonably good agreements are obtained.

This paper concerns the identification of the characteristic modes of the "Andreanov tsunami" based on the recently developed time-dependent Hilbert-Huang Transformation. Results of this technique are evaluated with conventional analysing methods based on the Fourier Transformation, e. g. restraining high and band pass filters which attempt to classify a signal into predefined frequency bounded subcategories. The Hilbert-Huang Transformation (HHT) disintegrates two (three) accurate monochromatic components from the collected data of the "Andreanov tsunami" in the near-field of the epicenters in shallow water environment which are assumed to characterize resonant effects as a result of tsunami-shoreline interaction processes. Furthermore the HHT determines a distinct time-frequency representation of the tsunami in the far-field of the epicenters in deep waters.

Accurate water level forecasts are of vital importance along the Gulf of Mexico as its waterways play a critical economie role for a number of industries including shipping, oil and gas, tourism, and fisheries. While astronomical forcing (tides) is well tabulated, water level changes along the Gulf Coast are frequently dominated by meteorological factors. Their impact is often larger than the tidal range itself and unaccounted for in present forecasts. We have taken advantage of the increasing availability of real time data for the Texas Gulf Coast and have developed neural network models to forecast future water levels. The selected inputs to the model include water levels, wind stress, barometric pressures as well as tidal forecasts and wind forecasts. A very simple neural network structure is found to be optimal for this problem. The performance of the model is computed for forecasting times between l and 48 hours and compared with the tide tables. The model is alternatively trained and tested using three-month data sets from the 1997, 1998 and 1999 records of the Pleasure Pier Station located on Galveston Island near Houston, Texas. Models including wind forecasts outperform other models and are considerably more accurate than the tide tables for the forecasting time range tested, demonstrating the viability of neural network based models for the forecasting of water levels along the Gulf Coast.

A storm surge model based on the shallow water equations and solved by a finite difference scheme has been developed. This model is adapted from the original COMCOT tsunami simulation model developed by Liu's group at Cornell. The modified COMCOT model was first applied to simulate the storm surge generated by both Hurricane Iniki and Hurricane Iwa for model validation. Then the linear and nonlinear versions of the model along with or without bottom friction were tested, and the simulated results are compared in order to examine the nonlinear effects on the generation and evolution of storm surge in the Pacific Ocean. Our results show that the nonlinear effects including convective acceleration and the bottom friction terms are not significant in storm surge modeling for the Pacific insular environment.

The U.S. Army Corps of Engineers' ADvanced CIRCulation (ADCIRC) model is applied to simulate the storm surge generated by Hurricane Iniki in Hawaii. The purpose of this study is to examine the validity of the ADCIRC model in predicting hurricane-generated storm surge in the Pacific insular environment and to investigate the sensitivity of storm surge generation to different wind models for this particular region. The simulated results showed good agreement with the recorded storm surge near the southwest shore of Kauai Island where Iniki made landfall. Our present numerical results revealed that the dominant forcing factor for the storm surge generation by Hurricane Iniki in Hawaii is the drop in atmospheric pressure near the eye of the hurricane, while the wind-generated surface stress has little direct effect in generating the surge.

The influence of natural sea states on wave overtopping constitutes one of the investigated aspects within the German research project "Loading of the Inner Slope of Seadikes by Wave Overtopping" (BMBF KIS 009). In fact, the incident wave spectrum is influenced by the very complex morphology in shallow coastal zones like wadden seas and shallow forelands. Therefore, the wave spectra in these areas are quite different from the commonly used theoretical single peak wave spectra. Wave run-up and wave overtopping are influenced by the shape of these wave spectra and can not be simply described on the basis of theoretical single peak wave spectra like PM, JONSWAP or TMA wave spectra. The objective of this paper is to study experimentally the influence of different wave spectra on wave overtopping for seadikes by means of small and large scale model tests. For this purpose, model tests were run for the following boundary conditions: (i) Regular waves, (ii) TMA-spectra (single peak), (iii) JONSWAP-spectra (single peak and double peak spectra composed of two superposed JONSWAP-spectra) and (iv) Measured single, double and multi peak spectra from different locations at the German and Dutch coast. The investigated wave spectra were provided by Dipl.-Ing. H.D. Niemeyer (Coastal Research Station, Norderney) and Dipl.-Ing. J. Grüne (Coastal Research Centre, Hannover) for several locations at the German North sea coast, by Dipl.-Ing. H. Bergmann (LWI) for Probstei / Baltic Sea, by Dipl.-Ing. T. Trampenau (LWI) for Warnemünde / Baltic Sea, by ir. John G. de Ronde (Rijkswaterstaat) for several locations in the Netherlands. Their contributions are gratefully acknowledged. The support of the german ministery of education and research (BMBF) within the project BMBF-KIS 009 is also gratefully acknowledged.

Sea dikes are used as coastal defence structures in many countries worldwide and have been subject to rigorous study. However most of the previous work and indeed the resultant design formulae for wave run-up and overtopping have been based on 2D testing and field measurements. This current study combined both 2D and 3D tests at different scales such that the influence of such parameters as wave direction and directional spreading could be examined. The results show that these parameters have a significant influence on both the run-up heights and overtopping volumes.

Recent topographic surveys of the breakwaters for Los Angeles/Long Beach Harbors revealed an average crest elevation of the San Pedro Breakwater of approximately 1.5 ft below the design crest of + 14 ft MLLW. A physical model study was conducted to estimate future impacts on harbor operations if crest loss continues or if the crest is restored to the design elevation. A 3-dimensional distorted-scale physical model (1:100 vertical, 1:400 horizontal) was used to investigate the change in total energy and low frequency wave energy (periods > ∼85 sec) at numerous locations within the harbor as a function of the breakwater crest elevation. Constraints of the distorted scale model were overcome to generate incident overtopping waves that induced low frequency oscillations in the harbor. Sensitivity of these oscillations to crest elevation is presented.

The origin of seiches in the Port of Rotterdam is investigated with observations at sea and in the harbour and with numerical simulations. A wavelet analysis of the observations shows that low-frequency energy (0.1–2.0 mHz) occurs at sea prior to each seiche in the Port of Rotterdam. An analysis of weather charts (from 1995 till 2000) indicates that all seiches coincided with the passage of a storm. Some of these storms included a sharp cold front, whereas others included a more gradual cold front. Numerical simulations with a hydrodynamic model driven by meteorological observations reproduced seiches for the sharp cold fronts but not for the gradual cold fronts.

Florida's St. Johns River Water Management District requires tidal constituents (amplitudes and phases) at open water boundaries on the continental shelf from the Florida/Georgia border to Jupiter, Florida. These tidal constituents are used as boundary conditions for hydrodynamic studies on the continental shelf and within estuaries. Since the historical tidal record is limited, this research (the production of the necessary tidal constituents) will result in the improvement of the accuracy of future coastal and estuarine simulations. A significant part of the overall effort was to refine an existing unstructured mesh (Eastcoast2001) of the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean west of the 60° W meridian. Eastcoast2001 has been refined in three distinct areas: near the Florida shoreline, along the eastern Floridan Plateau-edge, and across the continental slope. Refinement is on the order of three in the shallow regions and 10 across the continental rise. The new mesh retains the bathymetric data of Eastcoast 2001 and incorporates more detailed shoreline data. Simulations were performed with a two-dimensional, finite element code for coastal and ocean circulation (ADCIRC-2DDI), which was forced with M₂, M₄, M₆, O₁, N₂, S₂, K₁, and steady constituents. Model verification is demonstrated by comparison of simulation results to historical tidal data.

Large-amplitude harbor seiches at Ciutadella on Menorca Island in the western Mediterranean are related to local atmospheric conditions and it has been suggested that the seiche forcing mechanism involves the transfer of atmospheric energy to baroclinic modes in offshore waters. To explore this concept we examined the relationship between seasonal patterns of harbor seiche activity and water temperature. Results indicate that during the season of harbor water cooling, the probability of large harbor seiche activity varies linearly with water temperature. During the season of water warming, however, the probability of large seiche activity varies exponentially with the rate of water warming which is maximum at the summer solstice. These patterns in large seiche activity are in accord with published accounts and may result from seasonal changes in near-surface density stratification of the water offshore of Ciutadella.

This paper shows that the subtidal energy on the Texas Coast and in Corpus Christi Bay is large due to meteorological events and that the water level anomaly can be larger than the astronomical tide itself. The relative importance of remote and local forcing on the subtidal response in Corpus Christi Bay was studied using water level and wind data observed during the winter and spring months from 1998 to 2000. The multiple coherence squared between the water level response inside the bay and the local and remote forcing was high (MCS > 0.8 for most locations), indicating that the local wind stress and water level on the coast are the primary forcing mechanisms inside the bay over the range of frequencies studied. The study further confirmed the importance of remote forcing for the water level response as predicted by the analytical model of Garvine.

This paper discusses the analysis and results of an investigation into pressure field impacts caused by deep-draft vessel navigation on the beaches and bluffs along the Corpus Christi Ship Channel (CCSC), Corpus Christi, TX. A steady-state, 3-D hydrodynamic numerical model was modified to analyze the pressure fields generated by deep-draft vessels in the channel. The modified Vessel Generated Pressure Field (VGPF) simulates pressure field distributions and calculates water surface elevations in the channel during deep-draft vessel passage. The model incorporates the channel geometry (flat, shallow banks and deep center channel) and vessel geometry (length, beam, draft and position in channel). The vessel-generated pressure fields cause long-period water surface elevation fluctuations as large as one meter in height and 120 seconds in period. To validate the model, several field experiments were conducted that consisted of measuring the pressure waves during deep-draft vessel passage and tracking the positions and speeds of these vessels during a two-week period in August 2000. Data were collected continually during this period using a non-directional pressure gage deployed along the channel bank at elevation –2 meters (MSL). Since the channel banks are relatively flat (∼50H:1V), the water recedes far from the bluff when the drawdown passes, then rushes up in the form of long-wave runup with a bore on the leading edge. The results of the study have been used to identify the impacts of deepening the channel on shoreline stability and develop shoreline protection measures along the CCSC where pressure field effects have caused erosion of the beach and bluffs.

This paper introduces a closed-form analytical solution of the one-dimensional (1D), depth-averaged linearized momentum and continuity equations that incorporates linear bottom friction and the non-linear wind stress. The solution describes wind-forced motion in a 1D basin with horizontal bottom as governed by water depth, basin length, bottom friction coefficient, wind speed, and fundamental frequency of an oscillatory wind. The solution displays in compact form general behavior and dependencies of the physical processes, including generation of wind-induced harmonies of the forcing motion, damping, and resonance. The solution can serve as a benchmark test for numerical models of the shallow-water equations, as well as provide estimates of wind-induced motion in enclosed water bodies.

A weakly nonlinear analysis of two-dimensional, standing waves in a rectangular basin of arbitrary depth is presented. The waves are resonated by periodic oscillation along an axis aligned with the wavenumber vector. First, linear analysis is pursued in order to determine the growth rate of the resonated wave as a function of the basin dimensions, mode number, forcing amplitude, and fluid parameters. The effects of viscosity and frequency mismatch (detuning) are considered. It is found that waves in transitional depth have the largest growth rates. Experiments are found to agree extremely well with the theoretical results. Second, cubic nonlinearity is considered in order to describe limits on the maximum amplitude of the resonated wave that can not be accounted for by viscosity or initial detuning. Results indicate that, for the case of perfect resonance, the maximum amplitude can be two orders of magnitude larger than the forcing amplitude. Theoretical predictions of amplitude response curves confirm the nonlinear `frequency reversal' that has been demonstrated previously. Experiments again agree very well with the theory.

Based on extensive hydraulic model testing, the uncertainties of available standard models used to predict wave heights on shallow foreshores of coastal structures are quantified. Both wave transformation on the foreshore and at the structure are taken into account. Finally, improvements of the prediction models are proposed and recommendations on the selection of the models to be used are provided.

The evaluation of design waves for coastal protection structures is enormously important for both the safety of the hinterland and economical use of public money. The recently gained advancements in mathematical modeling of waves allows its successful application even in areas with complex morphological structures like the Wadden Sea. A remaining major problem of coastal design wave modeling is still the evaluation of suitable boundary conditions for design conditions, particularly for offshore design waves. The following paper highlights procedures applied for the solutions of these problems in the Frisian Wadden Sea at the south North Sea coast which are partly also applicable at coastlines of any type.

A comprehensive experimental study was conducted to produce benchmark wave kinematics data sets for moderate/steep regular and irregular waves. The experiments were conducted in a narrow glass-walled wave tank at Texas A&M University and velocities were measured using an LDV. The time series of surface elevation and wave kinematics were obtained at nine vertical positions including two points above still water level (SWL). The experimental data were compared with linear theory and fully nonlinear numerical wave tank (NWT) simulations based on potential theory, mixed Eulerian-Lagrangian approach, and boundary element method. For both regular and irregular waves, the linear theory tends to overestimate the measured kinematics especially above the SWL, and the fully nonlinear NWT simulations correlate better with experimental data. It is also shown that the exceedance probability for irregular wave crest heights is underestimated by the Rayleigh distribution, while the opposite is true for crest velocities. The joint distribution plots of wave crest/wave period and particle velocity/wave period reveal that there exists strong correlation between them.

Four laboratory datasets acquired in a directional wave basin and in a large-scale flume are re-analyzed to provide practical advice to coastal engineers in charge of estimating significant wave heights in the nearshore zone as part of a coastal structure design. An estimation of the total water depth including wave set-up and long wave activity is proposed. The underestimation of the significant wave height by using a spectral approach is stressed and rules of thumb are suggested to correct it.

The wave propagation model REFDIF was used to simulate wind-generated wave conditions in Dos Bocas Harbor to define breakwater modifications necessary to keep the harbor operational at least 85% of the time and to define the extreme wave climate in the harbor vicinity for one-berth and two-berth configurations.

The effects of defense structure on nearshore water flows are analyzed by means of an efficient and robust flow solver. This is both flexible enough to incorporate bathymetric data typically collected in field surveys and accurate enough to allow for a detailed description of important flow features. Such a tool is believed to be capable of providing useful information for design activities of coastal structures like submerged breakwaters.

Measurements of wave transmission at two trapezoidal submerged structures are analysed and discussed with respect to the design formula of d'Angremond et al.. Transmission coefficients agreed well within the given range of validity, however, an appropriate crest height and crest width from the rubble mound surface has to be used. Special interest has been put on results beyond the upper limit of the formula, e.g. relatively high water levels, the variation in the mean transmitted periods, and on some results from numerical modelling.

The Northwestern region of Egypt is characterized by its virgin nature with its all-original rural conditions without human interference. During the last few decades, the beach strips that overlook the waterfront have witnessed an urbanization revolution. The majority of the carried out installations fall within one single sector of investment, which locally called "Tourist Village". Human intervention in the coastal balance, by installation of different kinds of measures in the near shore zone, causes more diverse side effects and environmental deterioration. The unlucky shores subjected to erosion; one of these shores is located at about 140 km to the west of Alexandria and extends to about 1100 m. The shoreline change simulation for this shore is calibrated and modeled by GENESIS. The suggested protection measure was permeable groins. These groins, with its minimal effect on the adjacent shores, verify the requirements of Northwestern coastal protection policy. The proposed permeable groin is composed mainly of supported piles as main elements. In between each two piles, a wave screen is mounted. It is characterized by less water blocking, so it permits water flow exchange, and exerting slightly less total hydrodynamic force compared to a conventional pile groin. A construction system is designed to effectively reduce the installation time and in turn low cost. The modeling results and estimated cost show that the deterioration in the shoreline could be controlled with minimal side effects on the adjacent shores and with valued low cost.

This paper describes the procedures and results of a typhoon overtopping-frequency analysis for a vulnerable section of the commercial port road along Cabras Island, Apra Harbor, U.S. Territory of Guam. The study was a challenging application of present numerical modeling technology to an innovative project design.

The armor units on the rubble mound foundation of a composite breakwater should be of sufficient mass to ensure stability against storm waves. Toward this, the stability mass of seaward units has been calculated by an equation developed from hydraulic model tests and the mass of leeward units has been designed empirically as half mass of seaward units. This study uses numerical simulation to show that large eddies generated by wave overtopping results in a rapid caissonward flow above the leeward mound crown and that the velocity of this flow is a very important factor in the stability of armor units. Hydraulic model tests were used to formulate a function of wave conditions and structural geometry. From the balance of forces acting on an armor unit, the stability number N_s in the Hudson formula was formulated to allow design of armor units on the leeward mound.

This paper presents an analytical solution for the evaluation of linear wave interaction with a porous pile. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. The results show a clear reduction in wave heights when a permeable, rather than impermeable, structure is used. It is also seen that irregular waves generate smoother variations in the wave field than those predicted by the regular wave model.

Damages of coastal structures are often wave induced. A new study revealed that wave impact generated pressures can travel into water filled cracks or joints, thus damaging or destroying the structure from within. A series of experiments was conducted in QUB's wave channel to assess the characteristics of breaking wave impact induced pressure pulse propagation through partially water filled cracks. It was found that the pressure pulses generally travel at very low velocities of 45–70 m/s within completely submerged cracks, whereas velocities in partially submerged cracks are significantly higher. Pulses attenuate fast inside the fully submerged crack, but slowly in partially submerged ones. In partially submerged cracks the pressure pulse was found to travel in the air, propagating fast and with little attenuation deep into the structure, signifying that partially filled cracks are probably more dangerous man completely filled cracks. They are probably also the main cause for the seaward removal of blockwork in coastal engineering structures. This effect however is not limited to blockwork structures, but to every structure where cracks or joints occur, including natural rock cliffs.

This paper discusses wave processes that happen after a wave has impacted on a coastal structure. The paper gives, for the first time, measurements of the throw of overtopping waves at vertical seawalls / breakwaters, including their velocity / trajectory, and the loadings that result when overtopping water lands back onto the deck of the structure.

This paper presents results from collaborative research on Violent Overtopping of Waves at Seawalls (VOWS) describing overtopping performance and processes at steep seawalls. VOWS results have been used to develop / improve prediction methods for mean overtopping discharges, wave-by-wave overtopping volumes, and overtopping throw velocities. This paper discusses variabilities and uncertainties inherent in the overtopping processes, and presents example data on uncertainties to be used in probabilistic design or hazard evaluations. The dependency of these parameter uncertainties upon the proportion of wave overtopping waves is highlighted.

Wavelength of ocean waves and surf beat (infra gravity waves) has for the first time been computed as a function of frequency from different combinations of non-collinear 3-gauge arrays. Data at the 15-gauge polygonal array at 8m depth at Duck, North Carolina, USA, has been used. The method used is an extension of the 3-gauge method of Esteva 1976 & 1977 for computing wave direction. Wavelength was also computed using the Singular Value Decomposition (SVD) method of Herbers et al. 1995 from (i) κ_rms and (ii) κ_x, κ_y. The wavelength computed from the array measurements, using both the 3-gauge as well as the SVD(κ_x, κ_y) method, is nearly identical to the wavelength predicted by the well known dispersion relation for ocean waves (DROW), viz., (2πf)² = κg tanh κd, in the ocean wave regime (T ⩽ 11.64s spectral period); and is approximately thrice the predicted value in the surf beat regime (T ⩾ 32.00s). The implication of wavelength of surf beat at Duck being much larger than mat predicted by DROW, is that methods for determining the directional spectrum which use DROW can erroneously indicate a surf beat direction much closer (≅; 30° closer) to the shore normal than it actually is in the field. For example the variational method of Herbers et al. 1995 and the 2-gauge array method of Borgman 1974 are unfortunately both tainted with this error due to use of DROW.