Repository: Freie Universit├Ąt Berlin, Math Department

Regime of Validity of Sound-Proof Atmospheric Flow Models

Klein, R. and Achatz, U. and Bresch, D. and Knio, O.M. and Smolarkiewicz, P. (2010) Regime of Validity of Sound-Proof Atmospheric Flow Models. Journal of the Atmospheric Sciences, 67 (10). pp. 3226-3237. ISSN Online: 1520-0469 Print: 0022-4928


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Ogura and Phillips (1962) derived their original anelastic model through systematic formal asymptotics using the flow Mach number as the expansion parameter. To arrive at a reduced model which would simultaneously represent internal gravity waves and the effects of advection, they had to adopt a distinguished limit stating that the dimensionless stability of the background state be of the order of the Mach number squared. For typical flow Mach numbers of M = 1/30 this amounts to total variations of potential temperature across the troposphere of less than one Kelvin, i.e., to unrealistically weak stratication. Various generalizations of Ogura and Phillips' anelastic model have been proposed to remedy this issue, e.g., by Dutton & Fichtl (1969), and Lipps & Hemler (1982). Following the same goals, but a somewhat different route of argumentation, Durran proposed the pseudoincompressible model in 1989. The present paper provides a scale analysis showing that the regime of validity of two of these extended models covers stratification strengths of order of the Mach number to the power 2/3, which corresponds to realistic variations of potential temperature across the pressure scale height of about 30 K.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:835
Deposited By: Ulrike Eickers
Deposited On:08 Mar 2010 15:01
Last Modified:03 Mar 2017 14:40

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