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Weakly compressible flows I: regime of validity of sound-proof approximations

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Multiscale Numerics for the Atmosphere and Ocean

The design regime of established sound-proof flow models (anelastic, pseudo-incompressible) involves tropospheric flows at length scales of 10-100 km and associated advective time scales. Most derivations of such models require “weak background stratification” in some sense. In this lecture I demonstrate through arguments of multiple scales asymptotics that this constraint can be quantified: The anelastic and pseudo-incompressible approximations should be valid up to dimensionless potential temperature stratifications of the order of the Mach number to the power 2/3.

References:

Klein R., Achatz U., Bresch D., Knio O.M., and Smolarkiewicz P.K., Regime of Validity of Sound-Proof Atmospheric Flow Models, JAS vol. 67, pp 3226—3237 (2010)

Klein R., Scale-Dependent Asymptotic Models for Atmospheric Flows, Ann. Rev. Fluid Mech., 42, 249-274 (2010)

This talk is part of the Isaac Newton Institute Seminar Series series.

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