Journal of Waterway, Port, Coastal, and Ocean Engineering

Based on the second-order random wave theory, a joint statistical distribution of the sea surface displacement at a spatially fixed point and its time derivatives of order one and two are derived by using the characteristic function expansion method. From the joint distribution derived, a statistical distribution of the maximum sea surface displacement then is determined. The distribution is found to depend on the frequency spectrum of sea waves associated with the linear approximation and the second-order wave-wave interaction. It is noted that the distribution derived from the present work includes that derived from the linear wave theory as a special case. To demonstrate the nonlinear effect and the significance of the theoretical results developed, the maxima distribution of surface displacement of deepwater unidirectional waves is computed and compared with that obtained by the linear wave model.

The linearized theory of water waves is used to study the diffraction of an incident plane wave by a thin porous vertical breakwater of semi-infinite extent. Under the assumption that the wavelength is much greater than the breakwater thickness, the breakwater is replaced by a thin permeable barrier and a suitable boundary condition applied on the barrier. An explicit solution, found by the Wiener-Hopf technique, is presented for the barrier diffraction problem and then easily computable asymptotic forms are derived. Results are presented to illustrate the effects of porosity and variable angle of wave incidence.

This paper presents an analysis of a series of laboratory measurements of horizontal velocity and suspended sediment concentration (arrayed vertically) at a number of locations across a simulated shallow water bar built in fine sands (D₅₀ = 95 μm) and subjected to irregular waves of varying significant wave height but with a constant spectral shape (JONSWAP spectrum). Near the bar crest the net suspended transport rates, integrated between the lowest measurement point and the water surface (measured zone), are dominated by the time-averaged (current-induced) transport resulting from undertow. Away from the bar crest the net suspended sediment transport in the measured zone resulting from high-frequency oscillatory currents is important (and dominant) and directed offshore everywhere. Comparison of the measured suspended transport rates and those derived from bed elevation changes over time reveals significant fluxes in the unmeasured zone near the bed. These are inferred as being driven by high-frequency oscillatory transport very close to the bed and are critical for understanding bar morphological changes. Finally, the laboratory results are compared with results from field experiments.

A modified version of the CERC formula, which relates longshore sediment drift to deep water wave height and direction, has been used to define the equivalent wave height. The directional distribution of these wave heights and corresponding sediment transport rates and their analytical approximations are found using statistical analysis of high quality directional wave data measured simultaneously at two sites, Ashdod and Haifa. The directional distributions enable one to determine the directional shift between the average wave directions at both sites and to find the necessary corrections of wave directions at any location along the coast. The results emphasize the importance of accounting for wave directional shift in sediment transport calculations even when the locations are close. A detailed computation of directional shift for different ranges of wave heights is performed using correlation analysis of data sets. The corrections of wave directions at various locations along the coast are found by interpolation, and an excellent agreement between sediment fluxes at each location has been obtained when using the LITPACK package for littoral transport simulations with each data set.

The nonlinear dynamic interaction among water waves, composite breakwater and a sand seabed of finite thickness is studied experimentally and numerically in this work. Laboratory experiments were conducted to record the water surface levels around the breakwater and the dynamic pore-water pressure inside its base and seabed foundation. Two numerical models have been adapted to simulate the problem; boundary-element and finite-element method (BEM-FEM) and poro-elastic FEM models. The BEM-FEM model couples the wave field and the porous media governed by the fully nonlinear potential and modified Navier-Stokes equations, respectively. The BEM-FEM model predicts the waves transmitted through the porous media to the onshore side. The poro-elastic FEM model uses Biot's equations and runs under the effect of the surface pressure computed by the BEM-FEM model. It also considers the caisson deformation and computes the dynamic stresses in the poro-elastic media. The dynamic pore-water pressures computed by the poro-elastic and BEM-FEM models have been compared with the experimental records. The BEM-FEM model has been revealed to predict accurately the wave field. Moreover, the dynamic response of a composite breakwater and its seabed foundation at different wave stages is discussed.

From the analysis of an extensive series of two-dimensional and three-dimensional hydraulic model tests on the overtopping response of various types of caisson breakwaters, general design formulas and graphs have been derived. Exponential relationships relate the mean discharge and the percentage of overtopping waves with the relative freeboard. The parametric influence of geometrical changes and of wave obliquity and multidirectionality is described by reduction factors referred to the case of simple vertical structure under long-crested head-on wave attack. Comparisons are made with the three-dimensional overtopping response of sloping structures. Overtopping volumes per wave have also been measured and their distribution fitted with a universal probability function. Even the effects of overtopping waves on pedestrians behind the crownwall were statistically evaluated to allow an upgrading of the existing criteria for the admissible rates over breakwaters.