Journal of Waterway, Port, Coastal, and Ocean Engineering

The commercial computational fluid dynamics model FLOW-3D (Flow Science, Inc., Santa Fe, N.M.) is used to simulate two-dimensional wave transformation and breaking across a naturally barred beach profile. Fine scale pressures and velocities are computed for a $35.5\min$ period over a two-dimensional beach profile measured during the 1990 Delilah field experiment. The model is driven by observed wave spectra obtained in $8\mathrm{m}$ water depth, and results compared with a cross-shore array of pressure sensors and current meters extending from near the shoreline to beyond the surf zone and the spatial distribution of wave breaking patterns obtained from video data. In the calculations, wave breaking is a natural consequence of the fluid dynamics and does not require the use of empirical formulations or breaking criteria. Good agreement between modeled and observed wave height transformation, mean cross-shore flow, and wave breaking variability suggests that the model can be used as a numerical laboratory to study the wave breaking and dissipation process in detail, and perhaps lead to improved parametrizations for more computationally efficient numerical models.

The present work involves the investigation of the influence of wave height, wave period, water depth, and sea-ward slope on the stability, wave runup, and wave rundown of statically stable rubble-mound berm breakwater. The weight of armor stones used in the present study is 20% lighter than the weight that is required for a conventional breakwater, designed using Hudson formula for a wave height of $0.1\mathrm{m}$ in the model. In the present work models with a berm width of $0.6\mathrm{m}$ , at constant depth of $0.32\mathrm{m}$ from the seabed were tested. The damage to the breakwater model with the berm was compared with the results on a model without the berm using different armor weights. The variation of relative runup and rundown was found for different values of wave steepness and water depths in front of the structure. The damage to the breakwater, wave runup, and rundown for the structure with seaward slope 1:2 and 1:1.5 were compared. The investigation was carried out in the Marine Structures Laboratory, Department of Applied Mechanics and Hydraulics, National Institute of Technology Karnataka, Surathkal.

A time-averaged probabilistic model is developed to predict irregular wave runup statistics on permeable slopes such as cobble beaches and revetments. The cross-shore variations of the mean and standard deviation of the free surface elevation and horizontal fluid velocities above and inside a porous layer are predicted using the time-averaged continuity, momentum, and energy equations. The mean and standard deviation of the shoreline elevation measured by a runup wire are estimated from the predicted mean and standard deviation of the free surface elevation. The wave runup height above the mean water level, including wave setup, is assumed to be given by the Rayleigh distribution. The wave reflection coefficient is estimated from the wave energy flux remaining at the still water shoreline. This computationally efficient model is shown to be in fair agreement with 57 small-scale tests conducted on $1∕5$ and $1∕2$ permeable slopes situated inside surf zones on impermeable gentle slopes.

A meshless numerical model for nonlinear free surface water waves is presented in this paper. Using the fundamental solution of the Laplace equation as the radial basis functions and locating the source points outside the computational domain, the problem is solved by collocation of boundary points. The present model is first applied to simulate the generation of periodic finite-amplitude waves with high wave steepness and then is employed to simulate the modulation of monochromatic waves passing over a submerged obstacle. Very good agreements are observed when comparing the present results with an analytical solution, experimental data, and other numerical results.

Modeling of nearshore flows by means of the classic nonlinear shallow water equations is reviewed and analyzed with a specific focus on the interdependence between physical phenomena, model equations, and numerical schemes. Numerical benchmarking solutions for coastal applications are summarized. Strengths and limits of the nonlinear shallow water equations to reproduce the fundamental features of coastal flows are illustrated along with indications on needed improvements.

The Boussinesq equations are often used to simulate irregular nonlinear wave propagation in finite water depth. The mild slope equation is also frequently used for modeling regular linear wave propagation as there is no water depth restriction on it. In this paper a different approach is presented to derive a new set of equations. The Stokes first-order solution is used as a first approximation of distribution for velocity potential function or velocity over water column, and subsequently a new distribution function is derived. The new distribution function is then used to derive a new set of equations. For regular wave the linear dispersion relationship can be satisfied completely over entire range of water depth for the new equations. The shoaling gradient coefficient of the new equations is in good agreement with the theoretical value from the Stokes theory without water depth restriction. In finite water depth the new equations reduce to the improved Boussinesq equations. In very deep water the linearized new equations reduce to the classical wave equation. The new equations can be used for a regular wave propagating over the entire range of water depth taking into account the nonlinear effects in shallow water, or used for irregular waves in finite water depth. Numerical solutions of the new equations are compared with experimental data of regular and irregular waves. Good agreement is achieved.