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Ondes internes de gravité en fluide stratifié: instabilités, turbulence et vorticité potentielle

Abstract : A numerical study of the dynamics of internal gravity waves in a stratified fluid is carried out. We describe a parallel pseudo-spectral algorithm allowing the integration of the Navier-Stokes equations on a parallel computer. In two spatial dimensions,
we analyze the dynamics of an initially plane, monochromatic wave field of moderate amplitude. The wave field is unstable and breaks down, producing small scale turbulence influenced by stratification. The study is extended to the more realistic case of three spatial dimensions. In three dimensions, we study the same wave field,
perturbed with wave-like three-dimensional random noise, but we investigate
statically stable, as well as unstable waves (large amplitudes). It is shown that the
internal wave breaking is an intrinsically three-dimensional process, even for small amplitude waves. Three-dimensionalisation of the wave field occurs in zones where the density field is statically unstable. The gravitational collapse of a zone has a transverse structure in the plane perpendicular to the initial wave plane. The effect of small scale turbulence on the production of the non propagating part of flow, the potential vorticity mode, and on the production of a mean flow, allows us to conclude, that solely a small fraction of the initial total energy is converted into these two forms, the main part of the energy being dissipated by viscous dissipation as well as by heat conduction. We reconsider the potential vorticity mode in the light of non-canonical Hamiltonian dynamics of a stratified fluid. The derivation of a system of modified dynamics allows the investigation of the relaxation of a stratified flow, conserving its potential vorticity and its density, toward a stationary state of minimal total energy, corresponding to the potential vorticity mode.
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Contributor : Christophe Koudella <>
Submitted on : Saturday, April 24, 2004 - 9:22:18 PM
Last modification on : Thursday, November 21, 2019 - 2:21:56 AM
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  • HAL Id : tel-00005960, version 1


Christophe Koudella. Ondes internes de gravité en fluide stratifié: instabilités, turbulence et vorticité potentielle. Dynamique des Fluides [physics.flu-dyn]. Ecole normale supérieure de lyon - ENS LYON, 1999. Français. ⟨tel-00005960⟩



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