RESONANT REFLECTION AND REFRACTION-DIFFRACTION OF SURFACE WAVES DUE TO POROUS SUBMERGED BREAKWATERS

Abstract

A wave equation, taking account of the effects of porous medium, is transformed into coupled parabolic equations. It is assumed in the theory that the mean water depth and the thickness of porous layer are slowly varying and the bottom undulation is rapidly varying compared to the wavelength of surface waves. Though we can utilize the Bragg reflection to reduce transmitted waves behind breakwaters in one-dimensional case, wave heights behind breakwaters do not always decrease due to wave refraction-diffraction in horizontal two-dimensional case. By adding a dissipation term to the coupled parabolic equations, we can calculate the wave breaking deformation.