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| Titel |
Pseudo-incompressible, finite-amplitude gravity waves: wave trains and stability |
| VerfasserIn |
Mark Schlutow, Rupert Klein |
| Konferenz |
EGU General Assembly 2017
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 19 (2017) |
| Datensatznummer |
250138981
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| Publikation (Nr.) |
 EGU/EGU2017-2135.pdf |
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| Zusammenfassung |
| Based on weak asymptotic WKB-like solutions for two-dimensional atmospheric gravity
waves (GWs) traveling wave solutions (wave trains) are derived and analyzed with respect to
stability.
A systematic multiple-scale analysis using the ratio of the dominant wavelength and the
scale height as a scale separation parameter is applied on the fully compressible Euler
equations. A distinguished limit favorable for GWs close to static instability, reveals that
pseudo-incompressible rather than Boussinesq theory applies. A spectral expansion including
a mean flow, combined with the additional WKB assumption of slowly varying
phases and amplitudes, is used to find general weak asymptotic solutions. This
ansatz allows for arbitrarily strong, non-uniform stratification and holds even for
finite-amplitude waves. It is deduced that wave trains as leading order solutions can
only exist if either some non-uniform background stratification is given but the
wave train propagates only horizontally or if the wave train velocity vector is given
but the background is isothermal. For the first case, general analytical solutions
are obtained that may be used to model mountain lee waves. For the second case
with the additional assumption of horizontal periodicity, upward propagating wave
train fronts were found. These wave train fronts modify the mean flow beyond the
non-acceleration theorem. Stability analysis reveal that they are intrinsically modulationally
unstable. The range of validity for the scale separation parameter was tested with fully
nonlinear simulations. Even for large values an excellent agreement with the theory was
found. |
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