Shear waves in inviscid compressible fluids

Abstract

While elastic solids support compressional and shear waves, waves in ideal compressible fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. An exact analytic solution of linearized hydrodynamics equations is obtained that describes the shear waves in inhomogeneous, inviscid, compressible fluids with piece-wise continuous parameters in a uniform gravity field. The solution is valid under surprisingly general assumptions about the environment and reduces to some classical wave types in appropriate limiting cases. Free shear waves in bounded and unbounded domains as well as excitation of the shear waves by a point source are considered. Edge waves propagating along vertical and inclined rigid boundaries are found in rotating and non-rotating fluids. A possible role of the shear acoustic-gravity waves in a coupled ocean-atmosphere system is discussed.