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Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere

Wahlén, Erik LU and Schlutow, Mark (2020) In Mathematics of Climate and Weather Forecasting 6(1). p.97-112
Abstract
This study investigates strongly 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... (More)
This study investigates strongly 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/\sqrt 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. (Less)
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author
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organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Mathematics of Climate and Weather Forecasting
volume
6
issue
1
pages
97 - 112
publisher
De Gruyter
ISSN
2353-6438
DOI
10.1515/mcwf-2020-0105
language
English
LU publication?
yes
id
d29d17a2-f357-4cf0-acc5-565db82df31e
date added to LUP
2021-12-08 14:16:09
date last changed
2022-01-28 15:57:33
@article{d29d17a2-f357-4cf0-acc5-565db82df31e,
  abstract     = {{This study investigates strongly 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/\sqrt 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.}},
  author       = {{Wahlén, Erik and Schlutow, Mark}},
  issn         = {{2353-6438}},
  language     = {{eng}},
  number       = {{1}},
  pages        = {{97--112}},
  publisher    = {{De Gruyter}},
  series       = {{Mathematics of Climate and Weather Forecasting}},
  title        = {{Generalized modulation theory for strongly nonlinear gravity waves in a compressible atmosphere}},
  url          = {{http://dx.doi.org/10.1515/mcwf-2020-0105}},
  doi          = {{10.1515/mcwf-2020-0105}},
  volume       = {{6}},
  year         = {{2020}},
}