Wave interaction with an elliptic disc submerged in a two-layer fluid

Abstract

Wave interaction with a horizontal elliptic disc submerged in a two-layer fluid is studied here assuming linear theory. An elliptic coordinate system is used to solve the three-dimensional problem analytically. The fluid region is divided into a number of subregions and by means of separation of variables, velocity potential in each region is expressed in terms of series of Mathieu and modified Mathieu functions of real argument. Matching conditions along with the orthogonal properties of eigenfunctions provide solutions for the fluid velocity potentials. Numerical results are presented for the wave-induced forces and moments. The effect of variations in the depth of submergence of the disc, angle of incidence of the incoming wave, density ratio of the fluid and aspect ratio of the disc on these physical quantities have been analyzed. In particular, sudden amplification of forces and moments have been observed at certain frequencies when the disc is situated at close proximity to the interface. Various other behaviors of the solution are investigated in some detail.