The effect of pumping and ripples on the classical 2-D plane beach problem Original Research Article

Effects on gravity waves of forced percolation on a flat beach (the solution is derived only for beach angles View the MathML source where m ∈ N) are investigated in the framework of a classical nonhydrostatic model of a perfect fluid. The design percolation chosen in this simplified model (P) is based upon the velocity fluctuations in a nonpercolative model (NP) and is thus, spatially oscillatory with amplitude a decaying with depth of flow. It is shown for a certain choice of a that the logarithmic shoreline singularity of the classical incoming progressing wave can be made to vanish leaving a nonreflective wave having everywhere a finite amplitude. The first-order perturbation of NP for a slightly rippled impermeable beach is found to satisfy a P-type problem. We perturb the regular wave solution of NP problem with a regular perturbation.