Time-dependent water wave scattering by a bottom-mounted porous compound cylinder fitted with an annular porous lid

Abstract

In this work, we analyze the scattering of water waves by a fully submerged bottom-mounted concentric cylindrical system consisting of three components: an impermeable inner cylinder surrounded by a porous cylindrical wall and a porous lid covering the annular region. Consideration of a porous lid in the annular region gives rise to two different dispersion relations in two sub-regions which in turn present an additional complexity in the system in the form of evanescent modes. Locus of the propagating mode for free surface gravity wave follows an analogous path in the complex plane as the porous-effect parameter moves in its own complex plane, except for low frequency at which the path of the mode distorts significantly. The mean drift wave forces on the system are calculated numerically by using pressure integration method, and the effect of different set of physical parameters on the wave forces is also examined. The key finding of this analysis is that the wave force on the impermeable cylinder gets minimized for lower values of porous-effect parameter whereas the drift force on the outer porous wall gets minimized corresponding to higher values of porous-effect parameter. This work is also verified with an existing work in the literature and then extended to the time-dependent analysis. The plane incident waves with the Gaussian profile and the focused wave group are both considered in the time domain simulation.