Nonlinear and dispersive wave effects in coastal processes

Abstract

Numerical models are useful instruments for studying complex superposition of wave-wave and wave-current interactions in coastal and estuarine regions, and to investigate the interaction of waves with complex bathymetries or structures built in nearshore areas. The ability of the standard Boussinesq and Serre or Green and Naghdi equations to reproduce these nonlinear processes is well known. However, these models are restricted to shallow water conditions, and addition of other terms of dispersive origin has been considered since the 90's, particularly for approximations of the Boussinesq-type. Using the general wave theory in shallow water conditions, the different approaches commonly used in hydrodynamics studies in river systems, estuaries and coastal zones are initially addressed. Then, to allow applications in a greater range of shallow waters, namely in intermediate water conditions, a new set of extended Serre equations, with additional terms of dispersive origin, is presented and tested with available data in the literature. The hydrodynamic module, composed of the extended Serre equations, is then used as part of a morphodynamic model, which incorporates two more equations taking into account various processes of sediment transport. The wave velocity-skewness and the acceleration-asymmetry are taken into account and discussed based on numerical results and physical considerations.