Radiation of water waves by a heaving submerged disc in a three-layer fluid

Abstract

A thin rigid disc is submerged in the infinitely deep lower layer of a three-layer fluid. Using linear water wave theory, the three-dimensional problem of wave radiation due to heaving motion of the disc is considered. The problem is first reduced to solving a hypersingular boundary integral equation. This integral equation is then reduced to a system of one-dimensional Fredholm integral equations of second kind. The solution of each integral equation is associated with a radial component of the difference of potential function across the plate. The solution of these integral equations has been used to compute added mass and damping coefficient numerically. Numerical results for a heaving disc submerged in a single layer, a two-layer, and a three-layer fluid have been depicted. Also, the effects of different parameters like depth of upper layer, middle layer, distance of the disc from the interface, and the density ratios of the fluid layers on these physical quantities have been demonstrated.