Homotopy analysis of wave transformation over permeable seabeds and porous structures

Abstract

Based on the Homotopy Analysis Method (HAM), a semi-analytical solution method is proposed to solve the modified mild slope equation (MMSE) for waves propagation over permeable seabeds and porous structures. The present method overcomes the mathematical difficulties in treating the nonlinear dispersion equations introduced by the permeability effect, which limits the previous semi-analytical solutions to impermeable seabed and structures only. The proposed method is applied to both 1-D and 2-D axisymmetric wave transformation problems. The method is validated by systematically comparing the semi-analytical solutions of wave amplitudes and reflection coefficients against available experimental data and numerical results, demonstrating the method's capability for predicting wave transformation over both impermeable and permeable seabeds. It is ready to show that, for impermeable conditions, the present semi-analytical solutions degenerate into the earlier solutions without considering the porous effect. The semi-analytical solution method is further extended to examine the porous effects on wave transformation and reflection in various topographical conditions.