Journal of Waterway, Port, Coastal, and Ocean Engineering

The aim of this paper is to define a simple and useful formula to predict wave transmission for a common type of floating breakwater (FB), supplied with two lateral vertical plates protruding downward, named $\text{π}$-type FB. Eight different models, with mass varying from 16 to 76 kg, anchored with chains, have been tested in the wave flume of the Maritime Laboratory of Padova University, under irregular wave conditions. Water elevation in front and behind the structure has been measured with two arrays of four wave gauges. Our starting point for the prediction of wave transmission was the classical relationship established by Macagno in 1954. His relationship was derived for a box-type fixed breakwater assuming irrotational flow. Consequently, he significantly underestimated transmission for short waves and large drafts. This paper proposes an empirical modification of his relationship to properly fit the experimental results and a standardized plotting system of the transmission coefficient, based on a simple nondimensional variable. This variable is the ratio between the peak period of the incident wave and an approximation of the natural period of the heave oscillation. A fairly good accuracy of the prediction is found analyzing the data in the literature relative to variously moored $\text{π}$-type FBs, tested in small-scale wave tanks under regular and irregular wave conditions.

This paper presents the results of an experimental investigation of the backfilling of scour holes around circular piles. Scour holes around a pile are generated either by a current or a wave. Subsequently, the flow climate is changed from current to wave, combined waves and current, or wave to a smaller wave, leading to the backfilling of the scour hole. The investigation has shed light onto the mechanism behind the backfilling process. The results show that the scour depth corresponding to the equilibrium state of backfilling is the same as that corresponding to the equilibrium state of scour around the pile for the same wave (or combined waves and current) climate. The time scale of backfilling has been determined as a function of three parameters, namely, (1) the Keulegan-Carpenter number of the initial wave or current (which generates the initial scour hole); (2) that of the subsequent wave, which backfills the scour hole; and (3) the Shields parameter associated with the latter wave, for live-bed conditions. In the case of the combined waves and current, the current-to-wave-velocity ratio is also involved. The time scale of the backfilling process is completely different from that of scour. The time scale of backfilling is much larger than that of scour when the Keulegan-Carpenter number associated with the backfilling is ${\text{KC}}_f<O\left(10\right)$ (typical wind farm application), while the time scale of backfilling can be smaller than that of scour when ${\text{KC}}_f>>O\left(10\right)$.

The effects of regular surface waves on the descent of instantaneously released sediments were investigated experimentally. The detailed wave characteristics, including wave height ($H$), wave period ($T$), and wave phase of release, were controlled systematically through a wave synchronization system. The results showed that the sediment cloud was passively advected by the wave orbital motion, and there was no significant phase lag between the sediments and surrounding water particles. The motion of the center of mass and the growth rate of the sediment cloud averaged over four representative wave phases of release were found to be similar to those in a stagnant ambient condition. However, a shift (in the range of $\pm H/2$) in the horizontal equilibrium position of the oscillatory motion was observed and could be related to the wave phase of release. A passive advection model was proposed to predict the motion of a sediment cloud in the wave environment by superimposing the wave orbital velocity onto the descent velocity of the sediment cloud induced by buoyancy excess. The prediction was found to be in reasonable agreement with the experimental data.

Far infragravity waves (FIGWs) with periods of 2–64 min can reduce the underkeel clearance for vessels in transit to ports and cause resonance in and around harbors and bays that amplifies low-frequency current flows. Sea level records from six tide gauges along the east coast of New Zealand and the Chatham Islands are compared with offshore weather systems and spectral statistics from the gravity wave (GW) band (including both sea and swell waves) from wave buoys and hindcast sources. An empirical formula to predict coastal FIGWs is developed, based on the offshore GW significant wave height, associated peak period, and spectral width parameter. This formula is able to explain the occurrence of most FIGW events, confirming that most of the FIGW energy arriving at the coast is directly associated with GW energy. However, several discrete events were not predicted by the technique, and reverse ray tracing was applied to explore the origin of these events. In the light of these findings, previously reported long wave events on the coast of New Zealand are reexamined using the newly developed long wave predictor.

A mesh-free and highly convergent radial basis function–based differential quadrature method (RBF-DQ) is implemented to simulate shallow water waves in the marine environment and open channels. RBF-DQ is applicable in waterways of regular or irregular geometries for the simulation of currents and tidal waves. The multiquadric (MQ)-type radial basis function is used for the purpose of this study. MQ radial basis function has one or two shape parameters whose values significantly affect the accuracy of the results. To find appropriate values of the shape parameters, a parameter estimation methodology is introduced based on cross validation. The accuracy of RBF-DQ is evaluated by two idealized numerical examples along with a field application for the Oresund Strait located between Sweden and Denmark. In each case, either analytical, numerical solutions from other software programs or measured data were taken as benchmark solutions. Results of this study show that RBF-DQ, unlike conventional polynomial-based DQ, can be applied to irregular domains for tidal wave simulation. The method has two main advantages; first, it is mesh free and does not need mesh generation; second, with many fewer nodes, the results obtained compared well with analytical and benchmark solutions of other numerical schemes.

An analysis of the run-up over different beach profiles is performed to evaluate the influence of the seabed shape on shore flooding. The analysis was carried out on the basis of numerical solutions of the nonlinear shallow water equations. The chosen solver was shown to provide reliable (both quantitatively and qualitatively) run-up results by comparing numerical solutions (of both solitary and regular waves) with the only available analytical solution forced by a localized topographic change. The run-up patterns on both a natural beach profile and three simpler and schematic profiles derived from it were evaluated. Different wave conditions (both random and groups) were used for a total amount of 96 different cases of inundation. Results are expressed in terms of both maximum ($Z_{\max }$) and steady-state ($Z_{\mathrm{steady}}$) run-up. It is found that both types of run-up depend on the offshore variable $\sqrt{H_0{L}_0}$, as suggested by several available studies, and that, for all tested cases, random waves induce the largest $Z_{\max }$ compared with the wave groups. The largest $Z_{\max }$ is induced by the composite-planar profile for both random waves and groups. An important similarity is found for both $Z_{\max }$ and $Z_{\mathrm{steady}}$ induced by all wave types over the natural and equilibrium profiles, giving further support to the use of an equilibrium profile as representative of the natural profile. Attempts at finding an equivalent planar beach highlight unavoidable difficulties in choosing such a profile and reinforce the idea that the concept of an equivalent planar beach cannot bridge dynamics occurring from the depth of closure to the run-up. More likely, such a concept is only suitable to describe dynamics that are local to the foreshore.

The sequential ballast water exchange problem is characterized by its combinatorial and computational complexity that must be resolved in transoceanic ship design and involves key technologies. Solving the problem is subjected to many safety criteria including ships’ intact stability, hull girder strength, fore and aft drafts, and bridge visibility, et cetera. The combinatorial and computational complexity of the problem grows exponentially with the growth of the problem’s scale. It has been verified that current existing approaches are not adequate in solving the problem for ships with small design margins of the sequential exchange performances. This paper presents a heuristic solution strategy for the problem that has been tested to be applicable to double hull tankers and bulk carriers with small sequential exchange design margins. A simplified algorithm is developed and presented in this paper. Numerical simulations are conducted using a 50,000 deadweight (DWT) double-hull product tanker. The results show that, compared with existing approaches, the proposed approach is superior in flexibility and capability of automatically obtaining improved solutions with better key performances of the ship.