An analytical study on oblique wave scattering involving flexible porous structures in a two-layer fluid

A complete analytical solution procedure is proposed here to work out the mixed boundary value problems associated with the oblique wave scattering problem involving either a complete elastic porous plate or a permeable membrane in both the cases of finite and infinite depth water in a two-layer fluid. Problems for two different velocity potentials with a phase difference are described in the upper half-planes. They are redefined as the solution potentials for the problems in the quarter-plane. A couple of novel integro-differential relations are constructed to connect the solution potentials of the redefined problems with auxiliary wave potentials. The subsequent potentials are solutions to relatively simpler boundary value problems for the modified Helmholtz equation, with structural boundary conditions of the Neumann type. The generalised orthogonal relation is then used to address the auxiliary wave potential problems analytically. The solution wave potentials are then derived in terms of these auxiliary wave potentials with the aid of the integro-differential relations. Further, explicit analytical expressions are derived for the significant hydrodynamic quantities such as energy reflection and transmission coefficients corresponding to the surface mode (SM) and interface mode (IM), respectively. Moreover, the deflection of the flexible porous structures is derived analytically. The scattering quantities in both SM and IM are presented graphically against the wavenumber and angle of incidence for various values of non-dimensional parameters involved in the structures.