Abstract
A parabolic approximation is applied to a mild slope wave equation, derived by Mase et al. (1994), considering rapid bottom undulations about the mean depth and the effects of seabed permeability. The resulting coupled parabolic equations are used to analyze wave transformations over two-dimensional bottom topography with rippled undulations. When the ripples are permeable, incident and reflected waves become small, due to the energy dissipation in the porous media, compared to the case of rigid ripples. Although a wave control by using the Bragg reflection is effective in one-dimensional case, wave heights behind the ripples cannot be always reduced due to the effects of refraction-diffraction in two-dimensional cases.
