Journal of Waterway, Port, Coastal, and Ocean Engineering

In the present work a new Boussinesq dispersive wave propagation model is proposed. The model is based on a system of equations expressed in terms of the free-surface elevation and the depth-averaged horizontal velocities. The approach is developed for fully dispersive and weakly nonlinear irregular waves propagating over any constant water depth in two horizontal dimensions, but it can also be applied in mildly sloping beaches with considerable accuracy. The model in its two-dimensional formulation involves in total five terms in each momentum equation, including the classical shallow water terms and only one frequency dispersion term. The latter is expressed through convolution integrals, which are estimated using appropriate impulse functions. The formulation is fully explicit in space and thus no inversion is required for the numerical solution. The model is applied to simulate the propagation of regular and irregular waves using a simple explicit scheme of finite differences. Numerical integration of a convolution integral is also required. The results of the simulations are compared with experimental data, as well as with linear and nonlinear wave theory. The comparisons show that the method is capable of simulating weakly nonlinear dispersive wave propagation over finite constant or slowly diminishing water depth in a satisfactory way.

This paper describes the development of an efficient scaled boundary finite-element model (FEM) for the simulation of short-crested wave interaction with a concentric porous cylindrical structure. By weakening the governing differential equation in the circumferential direction, the SBFEM is able to solve analytically the weakened equation in the radial direction. Only the cylinder boundary on the circumference of the exterior porous cylinder is discretized with curved surface finite elements, while a complete analytical representation is obtained for the radial differential equation. Comparisons of the numerical results on wave diffraction forces and surface wave elevations at the cylinder to available analytical solutions demonstrate that excellent accuracy can be achieved by the SBFEM with a very small number of surface finite elements. The influence of varying the wave parameters as well as the system configuration on the system hydrodynamics, including the wave force, wave run-up, and diffracted wave contour is examined and extensive results on them are presented. This parametric study will help determine the various hydrodynamic effects of a concentric porous cylindrical structure.

The horizontal, lateral, and vertical velocity components in a recirculating channel were measured to study changes in the turbulent intensity, Reynolds stress, and velocity distributions due to the interaction between a current and gravity waves. These physical quantities for waves following and opposing a current were obtained by analyzing the velocity data taken during 250 wave cycles. The phase-averaged RMS values of horizontal and vertical turbulent intensities for the larger waves seem to decrease from those for the smaller waves at most elevations above the bed, although the analyzed data are scattered in the measured range. The direction of wave propagation to the current mostly influences the essential features of the resultant Reynolds stress and the general characteristics of the horizontal and vertical velocities. In this situation for the following waves, the mean velocities for the larger waves increase more rapidly from the bed to the mid-depth but decrease still more in the outer region. In contrast, the situation for the opposing waves reverses in the whole depth. The physical aspects from these measured horizontal velocities could be well described using the Eulerian mean velocity equation. Phase-averaged water surface variations for a combined wave and current motion are similar to those for the associated wave-alone motion, regardless of the relative directions of wave and current. The surface waves have sharp crests and long troughs when wave height is larger or water depth is shallower. The distributions of mean velocity components and turbulent quantities, including the lateral and vertical turbulence intensities and the corresponding Reynolds stress, were derived from the velocity data in a lateral plane. The presence of the waves amplifies the magnitude of lateral turbulent intensities considerably near the sidewall but does not cause marked changes in their vertical profiles close to the center of the channel.

Instantaneous bed-shear stresses in shoaling waves are studied. The shear stress, or in nondimensional form the Shields parameter, is a classical basic forcing parameter in coastal engineering to calculate sediment transport due to wave motion. Based on our recent work on incipient motion of particles under shoaling waves, we became interested in the effects on the shear stress if $u_{\infty }$ is determined by a more arbitrary wave shape, such as when waves are shoaling. We therefore present a derivation of the Shields parameter ${\theta }_{wf}$ as a function of the waveform parameter $\Phi$ , which is a further generalization of Nielsen’s studies. The results indicate that shear stress distributions are modified depending on the waveform parameter. Based on laboratory observations, we are able to validate some of our findings. The use and quantification of ${\theta }_{wf}$ should be helpful in the formulation of sediment transport due to shoaling waves confirming the role of wave skewness and asymmetry.

A surface roller model, which captures incipient breaking and postbreaking behavior, is presented for the numerical simulation of spilling breakers. It is based on the corresponding model used in conjunction with Boussinesq-type equations and is applied on the two-dimensional, inviscid but rotational, free-surface flow resulting from the propagation and breaking of regular waves over constant slope beach. The numerical solution of the Euler equations, subject to the fully nonlinear free-surface boundary conditions and the appropriate bottom, inflow and outflow conditions, is facilitated by a hybrid finite differences and spectral method scheme. Results are presented for beach slope values of 1/50, 1/35, and 1/20, and corresponding Irribaren numbers of 0.12, 0.20, and 0.30, respectively. Breaking depth $d_b$ , breaking wave height, and free-surface elevation envelope results are in very good agreement with available experimental measurements and indicate that empirical formulas underpredict both breaking wave height and breaking depth. At the breaking point, wave speed is equal to $1.2{\left(g{d}_b\right)}^{1/2}$ , while the local Froude number increases with increasing Irribaren number. During postbreaking, the surface roller model generates appropriate vorticity at the breaking face of the wave but overestimates the undertow current in the surf zone.

Velocities and sand concentrations measured along 20 transects at the Field Research Facility (FRF) at Duck, North Carolina during October 16–23, 1997 are analyzed to examine the cross-shore and longshore suspended sand transport in the FRF pier depression. The suspended sand volume $V_s$ per unit bottom area remains large outside the surf zone in the depression. The depth-integrated offshore and longshore suspended sand transport rates are shown to be estimated as $a$ , $\overline{U}$ $V_s$ and $\overline{V}$ $V_s$ , respectively, where the empirical parameter $a$ is in the range of 0.1–0.4 in the depression, $\overline{U}$ is the cross-shore current and $\overline{V}$ is the longshore current. The offshore suspended sand transport rate at the end of the pier is estimated to be as large as $3.5{\text{m}}^3/\text{h}/\text{m}$ at the peak of a storm with an offshore significant wave height of 3.5 m. The sand transported offshore appears to have been supplied by the longshore sand transport toward the pier depression.