Potential vorticity conservation, hydrostatic adjustment, and the anelastic approximation

Abstract

The anelastic equations of Lipps and Hemler are examined for their ability to conserve potential vorticity (PV). The equations are shown to be "PV correct' in the sense that they conserve potential vorticity in a manner consistent with Ertel's theorem and with the assumptions of the anelastic approximation. The ability to conserve potential vorticity helps the anelastic system capture the integrated effect of the acoustic modes in Lamb's hydrostatic adjustment problem. This proptotype problem considers the response of a stably stratified atmosphere to an instantaneous heating that is vertically confined but horizontally uniform. The other versions of the anelastic approximation are examined for their PV correctness and for their ability to parameterize Lamb's acoustic hydrostatic adjustment process. -from Author