Incompressible Wave Motion of Compressible Fluids

We consider linear waves in compressible fluids in a uniform potential field, such as a gravity field, and demonstrate that a particular type of wave motion, in which pressure remains constant in each fluid parcel, is supported by inhomogeneous fluids occupying bounded or unbounded domains. We present elementary, exact solutions of linearized hydrodynamics equations, which describe the new type of waves in the coupled ocean-atmosphere system. The solutions provide an extension of surface gravity waves in an incompressible fluid half-space with a free boundary to waves in compressible, three-dimensionally inhomogeneous, rotating fluids.