Hydrostatic and Geostrophic Adjustment in a Compressible Atmosphere: Initial Response and Final Equilibrium to an Instantaneous Localized Heating

Abstract

Abstract The initial and steady-state response of a compressible atmosphere to an instantaneous, localized heat source is investigated analytically. Potential vorticity conservation removes geostrophic and hydrostatic degeneracy and provides a direct method for obtaining the steady-state solution. The heat source produces a vertical potential vorticity dipole that induces a hydrostatically and geostrophically balanced cyclone–anticyclone structure in the final state. For a typical deep mesoscale heating, the net displacements required for the adjustment to the final steady state include a small, O(100 m) ascent of the core of the heated air with weak far-field descent and a large, O(10 km) outward/inward lateral displacement at the top/base of the heating. The heating initially generates available elastic and potential energy. The energy is then exchanged between kinetic, elastic, potential, and acoustic and gravity wave energy. In the final state, after the acoustic and gravity wave energy has dispersed,...