Propagation of perturbations in a two-layer rotating fluid with an interface excited by moving sources

Propagation of small perturbations in a two-layer inviscid fluid rotating at a constant angular velocity is studied. It is assumed that the lower density fluid occupies the upper unbounded half-space, while the higher density fluid occupies the lower unbounded half-space. The source of excitation is a plane wave traveling along the interface of the fluids. An explicit analytical solution to the problem is constructed, and its existence and uniqueness are proved. The long-time wave pattern developing in the fluids is analyzed.