Linear waves in a fluid flow with constant vorticity located under an ice blanket

Abstract

The linear dynamics of periodic waves on the surface of a fluid layer of finite depth located under an ice blanket which is simulated by an elastic plate is considered. The fluid particles in the unperturbed state move at a constant horizontal velocity, the profile of which has a linear shift along the vertical. It is shown that several type of waves exist which propagate at the same frequency. The number of waves depends on the frequency, the flow parameters in the fluid and the physico-mechanical parameters of the ice blanket. The problem of the diffraction of waves of fixed frequency on the edge of a semi-infinite elastic plate which floats on the surface of the fluid is considered. The problem is reduced to the solution of Laplace's equation in the strip with specified asymptotic forms at infinity and with boundary conditions on the sides of the strip which have a discontinuity at a point corresponding to the edge of the ice and contact-boundary conditions on the edge of the plate. The solution is constructed using the Wiener-Hopf method. The reflection and transmission coefficients of the waves across the edge of the plate are determined. The results obtained are analysed using the actual parameters of sea ice.