Bragg scattering of surface gravity waves by a submerged wavy porous plate

Bragg scattering of surface gravity waves by a slender pile-supported submerged wavy porous plate is studied under the assumption of small amplitude water wave theory. The waves past porous barriers are modeled using linearized pressure drop boundary condition known as Darcy law. Numerical solution for the boundary value problem is obtained using the Multi-Domain Boundary Element Method and the outcomes are validated with known results in the literature. For different wave and structural parameters such as the effect of the number of ripples of the wavy plate, effect of the relative ripple amplitude, relative plate length, plate porosities, and relative submergence depth; various physical quantities of interests like reflection and transmission coefficients, vertical force, and horizontal force coefficients are computed and analyzed. The study reveals that Bragg scattering occurs in the water of shallow and intermediate-depth for a wavy plate having more than two ripples and wave reflection increases with an increase in the amplitude of the wavy plate. For higher wavenumber or with an increase in plate length, Bragg scattering with harmonic and sub-harmonic peaks in the reflection coefficients are noticed in the case of wavy plate irrespective of permeability unlike the oscillatory decreasing pattern in the case of a flat plate. Wave forces exerted on the submerged plate decreases significantly with the introduction of structural porosity due to the dissipation of wave energy. Moreover, an increase in the number of ripples and ripple amplitude reduces the wave transmission; thus improving the overall performance for a wide range of frequencies. The study will be useful in the design of effective breakwaters for mitigating wave effects in the marine environment.