Compressible Convection in a Rotating Spherical Shell - Part Three - Analytic Model for Compressible Vorticity Waves

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Scientific paper

A simple analog to compressible convection in a rotating spherical shell is described and solved analytically to enable us to understand the basic physics of the prograde phase velocities that resulted from the numerical calculations of Paper II. The analog is for an inviscid, adiabatically stratified, rotating, equatorial annulus of gas for which a form of potential vorticity is conserved. Linear perturbations in this system take the form of vorticity waves which propagate prograde relative to the rotating reference frame as long as the density decreases outward. Their frequencies depend on the longitudinal wavenumber and density stratification in the same way as the convective modes of Paper II. Simple physical arguments explain these dependences.

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