Repository: Freie Universität Berlin, Math Department

Generalized modulation theory for nonlinear gravity waves in a compressible atmosphere

Schlutow, M. and Wahlén, E. (2019) Generalized modulation theory for nonlinear gravity waves in a compressible atmosphere. arXiv . (Submitted)

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Official URL: https://arxiv.org/abs/1911.12669

Abstract

This study investigates nonlinear gravity waves in the compressible atmosphere from the Earth's surface to the deep atmosphere. These waves are effectively described by Grimshaw's dissipative modulation equations which provide the basis for finding stationary solutions such as mountain lee waves and testing their stability in an analytic fashion. Assuming energetically consistent boundary and far-field conditions, that is no energy flux through the surface, free-slip boundary, and finite total energy, general wave solutions are derived and illustrated in terms of realistic background fields. These assumptions also imply that the wave-Reynolds number must become less than unity above a certain height. The modulational stability of admissible, both non-hydrostatic and hydrostatic, waves is examined. It turns out that, when accounting for the self-induced mean flow, the wave-Froude number has a resonance condition. If it becomes 1/2–√, then the wave destabilizes due to perturbations from the essential spectrum of the linearized modulation equations. However, if the horizontal wavelength is large enough, waves overturn before they can reach the modulational stability condition.

Item Type:Article
Additional Information:Preprint in arXiv:1911.12669
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group
ID Code:2388
Deposited By: Ulrike Eickers
Deposited On:09 Dec 2019 14:37
Last Modified:09 Dec 2019 14:37

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