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

Abstract

For water waves propagating over a permeable sea bottom, a one-dimensional modified mild-slope equation (MMSE) is briefly derived considering the effects of porous media and capable of describing a rapidly varying topography. The thickness of the porous layer is assumed to be infinite to reduce the computational cost. The present numerical model has been validated against Rojanakamthorn et al.’s (1989) experiment for waves transformation over a submerged permeable breakwater on an impermeable seabed, Mase and Takeba's (1994) numerical solution for waves over a porous rippled bed and Liu et al.’s (2020) analytical solution for wave propagation over a series of submerged trapezoidal bars, respectively. A good agreement is obtained. More computational results show that the wave energy will be dissipated in the permeable bottom, and it will achieve the maximal values near the positions of Bragg resonant reflection. The peak Bragg resonance increases with an increasing number of bars and bar slope. However, it decreases with an increase in the permeability, bar submergence, and slope of the seabed. Moreover, there exists a particular value of the bar width that maximizes the Bragg resonant reflection.