Linear waves propagating over a rapidly varying finite porous bed

Abstract

Using Green's second identity, extensions of the time-dependent and time-independent mild slope equations (MSE) are derived based on the equation for waves on a finite porous bed. For practical purposes, an energy dissipation term is included. The model is widely applicable and computationally inexpensive, especially for modelling submerged porous breakwaters, and is also capable of describing known scattering properties of porous ripple beds. For specific conditions, the model gives the same solution as those previously presented by other authors. The validity of the model is tested through comparison with those of other equations for a permeable rectangular breakwater and a rippled porous bed [Mase, H., Takeba, K., 1994. Bragg scattering of gravity waves over a porous rippled bed, Proc. 24th ICCE. ASCE, Kobe, Japan, pp. 635–649], as well as with experimental data for a trapezoidal permeable breakwater.