Water-wave induced groundwater pressure and flow in variable bathymetry regions and sandy beaches by an enhanced coupled-mode model

Abstract

An enhanced coupled-mode system is developed for modelling wave-induced pressure and groundwater flow in variable bathymetry coastal regions, in the layer under the permeable seabed. The sea bottom is assumed of general shape, characterised by sloping parts and undulations, without restrictions concerning mildness of bottom slope and curvature. The present model is based on a simplified version of the storage and momentum equations, corresponding to large values of stiffness ratio of the porous medium, permitting prediction of wave-induced groundwater pressure and flow in the case when the elastic motion of the seabed is very small and could be approximately neglected. The representation of the wave pressure field is based on a local-mode series expansion in the water column and the porous medium, consisted of propagating and evanescent modes, and defined by formulating and solving vertical eigenvalue problems at each local horizontal position. The latter series is enhanced by appropriate terms (the sloping-interface mode) enabling consistent satisfaction of the interface conditions at the seabed and providing fast convergence. Numerical results are presented and compared against predictions by other methods and measured data, illustrating the applicability of the present model to variable bathymetry coastal regions and sandy beaches.