Pulsating source in liquid under ice cover in the presence of shear flow

This paper presents a solution of the two-dimensional non-stationary problem of the development of wave motion in a two-layer liquid 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 in thickness. Dispersion dependences were determined for three wave modes arising in the presence of shear flow. The vertical deflections of the ice cover due to a pulsating source of disturbances located in an initially motionless layer of liquid were calculated. A special case is also considered where the liquid is bounded at the top by a solid lid. The problem is considered in a linear formulation, and the liquid is assumed to be ideal and incompressible.