Elastic Bottom Effect on Trapped Waves in a Two-Layer Fluid

Abstract

In this paper, a hydroelastic model is considered to examine the trapped modes supported by a horizontal submerged cylinder placed in either of the layers of a two-layer fluid flowing over an elastic bottom at a finite depth. The elastic bottom is modeled as a thin elastic plate and is based on the Euler–Bernoulli beam equation. Using multipole expansion method, an infinite system of homogenous linear equations is obtained. For a fixed geometrical configuration and a specific arrangement of a set of other parameters, the frequencies for which the value of the truncated determinant is zero are numerically computed and the trapped wavenumbers corresponding to those frequencies are obtained by using the dispersion relation. These trapped modes are compared with those for which the lower layer is of infinite depth. We also look into the effect of the variation of the elastic plate parameters on the existence of trapped modes. Significant difference is observed with respect to the existence and also in the pattern of the trapped modes between the present case and the one when the cylinder is placed in an infinite depth lower layer of a two-layer fluid.