A numerical model of wave run-up, overtopping, and regeneration is presented. The model (called OTT) is based on the one-dimensional nonlinear shallow water equations on a sloping bed, including the effects of bed shear stress. These equations are solved using a finite-volume technique incorporating a Roe-type Riemann solver. The main advantage of this approach over previously used finite difference solvers is that no special shoreline-tracking algorithm is required, so that noncontiguous flows can easily be simulated. Hence, this model can be used to simulate the transmission of waves over water surface-piercing obstacles. The numerical scheme and boundary conditions are described, and several existing data sets used to test the ability of the model to simulate wave transformation, run-up, and overtopping. Experiments of random wave (unimodal and bimodal) overtopping, presented here for the first time, indicate that the model performs much better than empirical formulas in predicting average overtopping ...

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.

Copyright 2012 Elsevier B.V., All rights reserved.Peer reviewedPublisher PD

This review highlights the important role of the depth‐averaged sediment concentration (DASC) to understand the formation of a number of coastal morphodynamic features that have an alongshore rhythmic pattern: beach cusps, surf zone transverse and crescentic bars, and shoreface‐connected sand ridges. We present a formulation and methodology, based on the knowledge of the DASC (which equals the sediment load divided by the water depth), that has been successfully used to understand the characteristics of these features. These sand bodies, relevant for coastal engineering and other disciplines, are located in different parts of the coastal zone and are characterized by different spatial and temporal scales, but the same technique can be used to understand them. Since the sand bodies occur in the presence of depth‐averaged currents, the sediment transport approximately equals a sediment load times the current. Moreover, it is assumed that waves essentially mobilize the sediment, and the current increases this mobilization and advects the sediment. In such conditions, knowing the spatial distribution of the DASC and the depth‐averaged currents induced by the forcing (waves, wind, and pressure gradients) over the patterns allows inferring the convergence/divergence of sediment transport. Deposition (erosion) occurs where the current flows from areas of high to low (low to high) values of DASC. The formulation and methodology are especially useful to understand the positive feedback mechanisms between flow and morphology leading to the formation of those morphological features, but the physical mechanisms for their migration, their finite‐amplitude behavior and their decay can also be explored.