Bragg resonant reflection of water waves by a Bragg breakwater with porous rectangular bars on a sloping permeable seabed

A modified mild-slope equation (MMSE) for waves propagation over a porous seabed is derived by using Green's second identity. The MMSE contains both the bottom curvature term and the slope-squared term. The model is computational inexpensive and capable of describing a rapidly varying porous bed. As an example, Bragg resonant reflection of water waves by a Bragg breakwater with an array of porous rectangular bars on a sloping permeable seabed is modeled numerically based on the present MMSE. At first, our numerical solution is validated against the analytical solution for shallow-water waves propagation over an impermeable Bragg breakwater and excellent agreement is obtained. Next, more computational results show that the primary peak Bragg resonance decreases with the increase of the permeability. It is also shown by the present results that the peak value of the primary Bragg resonance increases with increase of the bar number and the bar height. In addition, there exists a particular value of the bar width that maximizes the Bragg resonant reflection.