A new look at the pseudo-incompressible solution to Lamb's problem of hydrostatic adjustment

Abstract

The pseudo-incompressible solution to Lamb's problem of the hydrostatic adjustment of the atmosphere is revisited using a generalized formulation that allows time variation of the base state. It is found that the generalized pseudo-incompressible equations do reproduce the compressible solution of the nonlinear hydrostatic adjustment in the limit of small heating.