Action of a Pulsating Source in a Fluid in the Presence of a Shear Layer

The two-dimensional unsteady problem of the development of wave motion in a two-layer finite-depth fluid bounded from above by a free surface is solved. The cases in which one of the layers is at rest in the unperturbed state and in other layer (near-surface or near-bottom) the horizontal flow velocity varies linearly with depth are considered. The dispersion relations and the group velocities of three wave modes arising in the presence of shear flow are determined. The vertical displacements of the free surface caused by switching-on of a pulsating source located in the initially immobile fluid layer are calculated. The problem is considered in a linear formulation, the fluid is assumed to be ideal and incompressible.