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Etude expérimentale de deux tourbillons corotatifs

Abstract : This thesis deals with the experimental study of two parallel corotating vortices of equal circulation. The vortices are created in water by the impulsive movement of two flat plates, and are analysed using dye visualizations and Particle Image Velocimetry (PIV). We have created a PIV algorithm, optimized for flows with high velocity gradients, which translates the interrogation windows in a symmetric way, and deforms them according to the velocity gradients. At low Reynolds numbers, the vortices remain two-dimensional and laminar, and merge into a single final vortex in a three-stage mechanism: (1) the viscous growth of the core radii up to 24% of the separation distance, (2) the convective merging, i.e. the kinematic reorganization of the vorticity into a single core with spiral arms of vorticity, and (3) the axisymmetrization and viscous di_usion of the final vortex. The final vortex has a core size whose square is twice the square of the core size of the initial vortices. By analyzing the angular momentum of the filaments, we have constructed a model which predicts a destabilization of the vortex pair with a sudden decrease of the separation distance, when the core size exceeds a critical value. At high Reynolds numbers, the merging process is modified by the development of a three-dimensional instability, linked to an elliptic instability of the vortex cores, which creates a wavy perturbation of the vortex centerline inside an invariant stream tube. The growth rate and the width of the band of unstable wavelengths increase with the rotation of the vortex pair, and the experimental measurements are in good agreement with theoretical predictions. Merging of the vortices appears for smaller core sizes and leads to a bigger and more turbulent vortex than in the absence of a three-dimensional instability. At last, we analysed the evolution of a blob of dye in one of the vortices. At early stages, this scalar is subject to a hyperdi_usion process, due to the coupled presence of stretching and di_usion. A simple model predicts a temporal decrease of the scalar as t-3/2, but shows that the probability density function of the scalar is stationary, in agreement with the experimental result. At late stages, the probability density function of the scalar is not modified by the two-dimensional merging, but is displaced towards low values of the scalar in the case of turbulent merging, linked to the presence of high stretching rates in the three-dimensional flow.
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Submitted on : Wednesday, February 22, 2006 - 11:30:04 AM
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  • HAL Id : tel-00011665, version 1



Patrice Meunier. Etude expérimentale de deux tourbillons corotatifs. Dynamique des Fluides [physics.flu-dyn]. Université de Provence - Aix-Marseille I, 2001. Français. ⟨tel-00011665⟩



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