Journal of Waterway, Port, Coastal, and Ocean Engineering

The influence of local wind on nearshore breaking waves was investigated in a laboratory wave‐wind flume. The breaker location, geometry, and type were found to depend strongly upon the wind direction. Onshore winds cause waves to break earlier, to break in deeper water farther from shore, and to spill; offshore winds cause waves to break later, to break in shallower water closer to shore, and to plunge. For onshore winds, it was observed that breaking of the wind‐generated ripples can initiate spilling breaking of the primary underlying wave by providing a perturbation on the crest of the underlying wave as it shoals. The implications of these results are that surf zone width, currents, and sediment transport can be affected by local winds. Thus, engineering estimates of these quantities could be improved by consideration of local wind. Surf zone dynamics models that ignore wind or include wind only as a surface shear may be missing a very important effect of the wind—its effect on the initiation and mechanics of wave breaking.

A methodology for simulating nonstationary non‐Gaussian water levels on the Great Lakes is presented for use in providing input scenarios for erosion modeling on the Great Lakes. The methodology utilizes a low‐pass filtering technique to reduce the data to a stationary time series after which the data is transformed to a Gaussian series via use of the empirical distribution function coupled with a specialized tail‐fitting procedure for the extreme values in the data. The reduced series can then be resimulated in the frequency or time domain. The present series is resimulated in the frequency domain via a target spectrum, the spectrum of the reduced series. Inverse procedures are then utilized to simulate the original series. Comparisons of statistical and time series properties of the original and simulated series are made for a number of sites on the Great Lakes and it is found that the methodology provides a reasonable simulation for the original data.

The statistical distribution of zero‐crossing wave heights is considered within the context of a previous theory proposed by the writer some years ago. The underlying model, definitions, and assumptions are reexamined systematically to develop asymptotic approximations to the probability density, exceedance probability, and statistical moments of wave heights larger than the mean wave height. The asymptotic results have closed forms, and thus are easier to use in practical applications than the original theory, which requires numerical integration. Comparisons to empirical data are given to show that the present asymptotic theory produces the observed statistics of large wave heights faithfully to within 1%. Further, comparisons with other relevant theories also reveal that if one remains true to the theoretical definitions, then the present theory is the most accurate in predicting the exceedance distribution of large wave heights. Finally, the asymptotic theory is coupled with the statistics of wave periods to derive a theoretical expression for the joint distribution of large wave heights and associated periods. The predictive utility of this last result remains to be explored.

Three irregular wave test runs were conducted to obtain detailed data on irregular wave reflection and run‐up on a 1:3 rough impermeable slope. The test results were also used to evaluate the capabilities and limitations of an extended numerical model for predicting the time series and spectral characteristics of the reflected waves and waterline oscillations on the slope. The numerical model is shown to predict the measured time series and spectra reasonably well, including the selective nature of wave reflection and dissipation as well as the appearance of low‐frequency wave components in the waterline oscillations on the 1:3 slope. The numerical model extended herein may not be as accurate as hydraulic model tests but can be used to predict hydrodynamic quantities that are difficult to measure directly. Moreover, any incident irregular wave train including that measured in the field or generated numerically for given incident wave spectrum can be specified as input to the numerical model. This will avoid the difficulties associated with the reproduction of specified incident irregular waves in experiments.

The interaction of water waves with a long linear array of offshore breakwaters is examined to determine the reflection and transmission coefficients for these structures, providing data on the sheltering afforded by these structures. Two variational methods and an eigenfunction expansion method are used to determine the reflection coefficients for waves with wavelengths longer than the distance from gap to gap in the breakwater array. The eigenfunction method is also used for breakwaters, where the spacing between the gaps is longer than the water wavelength. For this case, analogous to scattering of light by a grating, numerous monochromatic directional wave trains can be generated in the region behind (and in front of) these breakwaters, which can lead to the generation of rip currents, beach cusps, and other periodic phenomena on beaches behind the structures.

This paper describes random wave forces acting on a fixed, slender, horizontal circular cylinder in the vicinity of the free surface, taking account of the intermittency of submergence and wave slamming. Expressions are derived for the probability density and the mean of the force maxima, and the calculation of the expected value of the single largest force maximum occurring within a given duration is also described. These various predictions are based on the assumptions of linear wave theory and a narrow‐band wave spectrum. Depending on the elevation of the cylinder and the wave height, the force maxima in individual waves may be associated with either inertia, combined drag‐inertia during complete submergence, the instant of complete submergence, partial submergence, or slamming. The probability density of force maxima incorporates force ranges within which the maxima are associated with one or other of these effects. Numerical results relating to these statistical properties are presented, and the effects of intermittent submergence and wave slamming are discussed.

Evaluation of the complete elliptic integrals and Jacobian elliptic functions can be made using power series in terms of the modulus, k, of the elliptic integrals, or in terms of the name, q, or complementary nome, q′, of the Theta functions. For the ranges of these parameters encountered in cnoidal wave theory, computations are much more efficient using q or f′. An approximate, explicit expression for q in first-order cnoidal wave theory is derived. Based on accuracy and computational efficiency, the expression is recommended for applications where the Ursell parameter is less than approximately 55. Isobe's approximate, explicit expression for q′ is recommended for applications where the Ursell parameter is greater than approximately 55. One or the other of these expressions is accurate over the entire range of Ursell parameter for which cnoidal wave theory is applicable. The explicit expressions for q and q′ are particularly useful for desktop calculations and for computationally intensive applications such as numerical models of the refraction and shoaling of cnoidal waves.