A Mathematical Model of Wave Transformation over a Submerged Breakwater

Abstract

A mathematical model of wave transformation over a submerged permeable breakwater is developed on the basis of the equations for waves on a permeable bed which are newly derived under the mild-slope assumption. Firstly the equation governing an unsteady flow in a porous medium is linearized using an approximate expression of the nonlinear friction term. Outside the porous medium, the linear wave theory is applied. Then integration of the equations in the vertical direction yields a two-dimensional elliptic-type equation analogous to the mild-slope equation on an impermeable bed. The equation can be solved numerically to evaluate wave transformation due to a submerged breakwater. The validity of the model is confirmed through comparisons with experiments for a trapezoidal breakwater and with strict solutions for a rectangular breakwater.