Modeling of Cross-shore Wave Propagation with Moving Shoreline

Abstract

A numerical model for the transformation of nonlinear waves in the cross-shore direction towards the shore is developed by incorporating a moving shoreline boundary condition. The shoreline formulation is based on the net volumetric change eected by the translating shoreline front. Initial numerical results indicated the need to recast the (ƞ; u) wave model to a (ƞ;Q) form to remove the numerical instabilities due to discretization of the physical shoreline condition. It is also imperative to apply a threshold depth at the moving front to avoid singularities due to the very small total depth at the last wet point. Subsequent numerical simulations of nonbreaking wave runup on a plane sloping beach indicate that the moving boundary treatment reproduces the important wave evolution features revealed by past analytic studies. Results of numerical simulations of wave runup-rundown induced by nonlinear incident waves on beach slopes as high as 1/20 show the applicability of the moving shoreline treatment and the reformulated wave model.