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Instabilités, turbulence et dynamo dans une couche de fluide cisaillée en rotation rapide. Importance de l'aspect ondulatoire

Abstract : By averaging the Navier-Stokes equation along the rotation axis, we developed an enhanced Quasi-Geostrophic (QG) model that is able to handle barotropic rotating fluid flows in an axisymmetric container with finite slopes. This QG-model is used to study the instabilities of a shear layer known as the Stewartson layer. We show that the slope is the key parameter of the instabilities, which are Rossby-waves. In addition to the bulk viscous term, a realistic Ekman friction derived from Greenspan's formula is implemented in our QG-model. This allows us to obtain highly turbulent flows with realistic dissipation at all scales, for a rapidly rotating fluid. We observe some interesting properties of the QG-turbulence generated by a highly unstable Stewartson shear layer, like very steep spectra (-5 power law, corresponding to Rossby-wave turbulence) and very steady regime. The previous flows produced by the destabilization of a Stewartson shear layer are used as input for a kinematic dynamo study, at moderate to very low magnetic Prandtl numbers (Pm). The main findings are that such flows are actually dynamos, which are quite easy to start; the dynamo action seems to extend to arbitrary low Pm, with a roughly constant critical magnetic Reynolds number (Rm). The wave-type nature of these flows is necessary to start a dynamo. Finally, we tried to implement the Lorentz force back reaction in the dynamo code. We found that the Rossby-wave nature of our turbulent flows does not allow us to use a diffusive approximation at small scales.
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Contributor : Nathanaël Schaeffer <>
Submitted on : Tuesday, October 18, 2005 - 7:24:08 PM
Last modification on : Tuesday, December 29, 2020 - 11:50:03 AM
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  • HAL Id : tel-00009743, version 3



Nathanaël Schaeffer. Instabilités, turbulence et dynamo dans une couche de fluide cisaillée en rotation rapide. Importance de l'aspect ondulatoire. Dynamique des Fluides [physics.flu-dyn]. Université Joseph-Fourier - Grenoble I, 2004. Français. ⟨tel-00009743v3⟩



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