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A new look at the pseudo-incompressible solution to Lamb's problem of hydrostatic adjustment
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@MISC{Almgren_anew,
author = {Ann S. Almgren},
title = {A new look at the pseudo-incompressible solution to Lamb's problem of hydrostatic adjustment},
year = {}
}
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Abstract
The pseudo-incompressible solution to Lamb's problem of the hydrostatic adjustment of the atmosphere is revisited using a generalized formulation which 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. 1 Introduction In a series of papers by Bannon (1995a,b; 1996) Lamb's problem of hydrostatic adjustment of the atmosphere is analyzed using the compressible equations and several dierent formulations of the anelastic approximation, including the pseudo-incompressible formulation (Durran 1989). The solution of the pseudo-incompressible equation with a time-independent base state is found to fundamentally dier from the solution of the compressible equations in both the linearized and nonlinear cases. In this note we demonstrate that if the base state pressure is allowed to vary with time, the correct equilibrium solution fo...
Keyphrases
hydrostatic adjustment pseudo-incompressible solution new look compressible equation several dierent formulation compressible solution time-independent base state nonlinear hydrostatic adjustment base state nonlinear case pseudo-incompressible formulation time variation correct equilibrium solution fo anelastic approximation small heating generalized pseudo-incompressible equation base state pressure pseudo-incompressible equation
