Axially symmetric motion of a stratified, rotating fluid in a spherical annulus of narrow gap

Abstract

A linear theory is presented for the steady, axially symmetric motion of a stratified fluid in a narrow, rotating spherical annulus with a spherically symmetric gravitational field.The fluid is driven by a combination of differential rotation of the two shells and differential heating applied at the surfaces of the spheres.It is shown that the effect of stratification becomes increasingly important at lower latitudes with the Ekman layers on the spheres’ surfaces fading in strength as the geostrophic interior velocities themselves tend toward the shell speeds at lower latitudes.The Singularities In The Geostrophic Solutions At The Equator Are Removed By A Boundary Layer Whose Detailed Structure Depends On The Ratio Of Horizontal To Vertical Mixing Coefficients Of Momentum And Heat.