Damping of ocean waves by a porous disk submerged in a two-layer fluid

Abstract

The wave interaction with a horizontal porous disk of negligible thickness submerged in either layer of a two-layer fluid is investigated. The solution of the wave scattering problem of the submerged disk is sought analytically by developing an eigenfunction matching approach and using linear potential flow theory. We derive a complex dispersion relation for both scenarios of the disk being placed in either layer, which is required to be solved to get the eigenvalues corresponding to the vertical eigenfunctions. The transition of the eigenvalues is analyzed for the first five solutions, shedding light on the underlying physical process of mode swapping that governs the dissipation mechanism due to porosity. The same algorithm is used to locate the required number of eigenvalues for computation. The effect of different parameters on different physical quantities is analyzed for both scenarios. Known results for a horizontal porous disk submerged in a finite-depth homogeneous fluid are recovered from the present analysis. A critical observation is the reduction in the maximum force amplitude (from 55% to 77%) with increasing values of the porosity parameter (from 2 to 20), demonstrating its enhancement influenced by porosity. In addition, we notice that the positioning of the disk near the free surface or the interface increases the wave force acting on the disk. Hence, the analysis makes it clear that the configuration of the disk plays a key role in maximizing the performance of the disk as a wave absorber.