Achatz, U. and Klein, R. and Senf, F. (2010) Gravity waves, scale asymptotics, and the pseudoincompressible equations. Journal of Fluid Mechanics, 663 . pp. 120147.

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Abstract
Multiplescale asymptotics is used to analyze the Euler equations for the dynamical situation of a gravity wave (GW) near breaking level. A simple saturation argument in combination with linear theory is used to obtain the relevant dynamical scales. As small expansion parameter the ratio of inverse of the vertical wave number and potentialtemperature and pressure scale heights is used, which we allow to be of the same order of magnitude here. It is shown that the resulting equation hierarchy is consistent with that obtained from the pseudoincompressible equations, both for nonhydrostatic and hydrostatic gravity waves, while this is not the case for the anelastic equations unless the additional assumption of sufficiently weak stratication is adopted. To describe vertical propagation of wave packets over several atmospheric scale heights, WKB theory is used to show that the pseudoincompressible flow divergence generates the same amplitude equation that also obtains from the full Euler equations. This gives a mathematical justication for the use of the pseudoincompressible equations for studies of gravitywave breaking in the atmosphere for arbitrary background stratication. The WKB theory interestingly also holds at wave amplitudes close to static instability. In the meanflow equations we obtain in addition to the classic waveinduced momentumflux divergences a waveinduced correction of hydrostatic balance in the verticalmomentum equation which cannot be obtained from Boussinesq or anelastic dynamics.
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:  888 
Deposited By:  Ulrike Eickers 
Deposited On:  25 Mar 2010 14:25 
Last Modified:  03 Mar 2017 14:40 
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