Angular Momentum Coordinates and Their Use in Zonal, Geostrophic Motion on a Hemisphere

Abstract

The equations of motion for balanced, axisymmetric motion on a hemisphere are transformed to a somewhat simpler form employing angular momentum as a new, meridional coordinate. The resulting equations may be regarded as a relative of the semi-geostrophic equations and have similar properties such as the stretching of zones of high vorticity. Wind and temperature fields may be obtained by solving an approximate linear equation given the Ertel potential given vorticity field and suitable boundary conditions.