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| Titel |
Radiative instability of a stratified Lamb-Oseen vortex |
| VerfasserIn |
X. Riedinger, S. Le Dizès, P. Meunier |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250027194
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| Zusammenfassung |
| In this presentation, we willl show that internal gravity waves generation can be explained by
the instability of a flow. A jet flow, a shear flow or a vortex flow, in presence of
stratification, may be subject to an instability which is radiative. We focus here on
the case of the stratified Lamb-Oseen vortex with a stratification along the vortex
axis.
Le Dizès and Billant1
have shown that, when the stratification is strong, the vortex is inviscidly unstable. The
unstable modes are radiative and extend far from the vortex core. Our objective is to analyse
the effects of viscosity and stratification on these unstable modes. A linear temporal stability
analysis is performed using a Chebychev collocation spectral code. The equations are the
linearized Navier-Stokes equations with Boussinesq approximation. The parameters are the
Froude number F = Ωmax-N and the Reynolds number Re = Î-(2Ïν) with Ωmax the
maximal angular velocity of the vortex, N the Brunt-Väisälä frequency, Î the vortex
circulation and ν the kinematic viscosity.
For fixed m (azimuthal wavenumber), k (axial wavenumber), F and Re the spectral code
provides the complex frequency Ï of the eigenmodes. By maximising the growth
rate Im(Ï) over the axial wavenumber, we obtain typical growth rate curves. The
instability is the strongest for a Froude number around one and the vortex remains
unstable for all Reynolds numbers. We shall explain that the stabilization for small
Froude number is due to the scaling in -1
F of the most unstable wavenumber and that
the stabilization for large Froude number is linked to the appearance of a critical
layer.
For intermediate Froude numbers, another instability mechanism responsible for growth
rate oscillations has been discovered. This new instability which will be explained in detail is
due to resonances between the radiative modes and the neutral modes of the unstratified
flow.
Experimental results are given. We tried to produce the most realistic Lamb-Oseen vortex
in a tank filled with a stratified fluid made using salted water. We found a destabilisation of
the vortex which creates an ondulation of the vortex axis. The wavelength and the value of the
Froude number at which the instability occurs are in correct agreement with the numerical
results. |
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