Oblique wave interaction with porous, flexible barriers in a two-layer fluid

Abstract

Oblique wave scattering by multiple porous, flexible barriers is studied in a two-layer fluid in both the cases of surface-piercing and bottom-standing partial barriers in water of finite depth. The mathematical problem is handled for a solution using a generalized orthogonal relation suitable for a two-layer fluid along with the least square approximation method for single and double barriers. Various characteristics of the eigensystem, including convergence of the eigenfunction expansions for the velocity potentials associated with surface gravity waves in two-layer fluid, are derived. Wave scattering by multiple barriers is studied using a wide-spacing approximation method and compared with the solution obtained through the least square approximation method in the case of double barriers. The effectiveness of the barrier system on wave scattering is analyzed in different cases by analyzing the scattering coefficients in surface and internal modes, surface and interface wave elevations, deflection of the flexible barriers under wave action, and wave loads on the barriers. It is observed that multiple zeros in wave reflections occur for waves in surface and internal modes for various values of nondimensional barrier spacing and an oblique angle of incidence. Further, the condition for Bragg resonance is derived in the case of multiple barriers in a two-layer fluid. In the case of wave scattering by double barriers, for certain combinations of barrier spacing and porous-effect parameter, optimum wave forces are exerted for the same angle of incidence. The findings of the present study are likely to play a significant role in the protection of marine facilities from wave action.