Water wave interaction with a submerged porous disc in a two-layer fluid

Using linear water wave theory, we consider a three-dimensional problem concerning the interaction of waves with a submerged porous disk in a fluid containing two layers of finite depth bounded above and below by a free surface and a rigid surface, respectively. The porous disk is positioned in the upper layer. The solution is based on the domain decomposition method to avoid the complex dispersion equation that often arises while studying porous structures, making it easier for numerical implementation. The velocity potentials are determined by the matched eigenfunction expansion method. The velocity potentials in those regions that contain the porous disk as a boundary have been decomposed into several components. Each component of the velocity potential is then expressed in terms of the eigenfunctions. Matching conditions and the orthogonal properties of eigenfunction assist in determining the velocity potential. The wave-induced forces and the amplitude of the propagating waves have been numerically analyzed. The variation in the wave-induced forces and amplitude of the waves above and below the disk, for different depths of submergence of the disk, density ratio of the fluid, and porous effect parameter of the disk has been analyzed. Sudden amplification and reduction of forces have been observed at certain frequencies. The numerical results show that, for low frequencies, the presence of an interface has a significant effect on the hydrodynamic coefficients. The results provide important insights for applications in offshore engineering, coastal protection, and environmental modeling, specifically in situations where porous materials interact with waves in multi-layered fluid systems.