PULSATING SOURCE IN A FLUID UNDER ICE COVER IN THE PRESENCE OF SHEAR FLOW

Abstract

This paper presents a solution of the two-dimensional unsteady problem of the development of wave motion in a two-layer fluid of finite depth under ice cover modeled by a thin elastic plate taking into account longitudinal compression forces. The cases are considered where, in the unperturbed state, one of the layers is at rest and in the other (top or bottom) layer, the horizontal flow velocity varies linearly over the thickness. Dispersion relations are derived for three wave modes arising in the presence of shear flow. Vertical deflections of the ice cover caused by the presence of a pulsating source of perturbations in the initially motionless fluid layer are calculated. A special case is also considered where the fluid is bounded at the top by a solid lid. The problem is considered in a linear formulation, and the fluid is assumed to be ideal and incompressible.