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Dynamique de l'appariement tourbillonnaire en milieu stratifie et stratifie tournant

Abstract : One of the main characteristics of geophysical flows is the presence of stable stratification, i.e the presence of a vertical density gradient. Such flows are generally organized into thin horizontal layers. This PhD thesis investigates numerically, theoretically and experimentally the dynamics of a pair of co-rotating vertical vortices in a stratified fluid in order to understand the mechanism of formation of such layered structure. Such flow is of high interest because co-rotating vortex pairs play an important role in two-dimensional turbulence through the merging process which leads to the energy transfer from small to large scales. A three-dimensional instability has been discovered. It is similar to the zigzag instability observed on a pair of counter-rotating vortices in a stratified fluid and it decorrelates the vortex merging along the vertical. A numerical three-dimensional stability analysis has shown that the zigzag instability dominates for strong stratification whereas the elliptic instability dominates for weak stratification. The zigzag instability bends symmetrically the two vortices without significant internal deformation. It selects a wavelength proportional to Fh b, where Fh is the horizontal Froude number and b the separation distance between the vortices. Its growth rate is proportional to the strain rate. An asymptotic analysis has recovered these scaling laws and has shown that the zigzag instability comes from the coupling between vortex bending modes and the strain field that each vortex generates on the other. Experimental observations and Direct Numerical simulations have also shown that the vertical lengthscale selected by the instability agrees with the predictions.of the stability analyses. The non-linear effects do not slow down the instability development but tends to recorrelate the fluid within each layers and to expel vertical gradients in between these layers. In the final part, the effect of planetary rotation has been investigated. It is shown that the zigzag instability remains active with a growth rate independent of the Coriolis parameter. In the rapidly rotating regime (quasi-geostrophic), the zigzag instability is similar to the "tall-column" instability with the most unstable wavelength proportional to Fh b / Ro, where Ro is the Rossby number. This instability may therefore affect geophysical flows for a large range of parameters both in the oceans and the atmosphere.
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Submitted on : Thursday, March 16, 2006 - 9:48:21 AM
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  • HAL Id : tel-00011962, version 1

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Pantxika Othéguy. Dynamique de l'appariement tourbillonnaire en milieu stratifie et stratifie tournant. Dynamique des Fluides [physics.flu-dyn]. Ecole Polytechnique X, 2005. Français. ⟨tel-00011962⟩

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