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Tilt-induced instability of a stratified vortex

Published online by Cambridge University Press:  17 January 2008

NICOLAS BOULANGER ,
PATRICE MEUNIER  and
STÉPHANE LE DIZÈS
NICOLAS BOULANGER
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, 49, rue F. Joliot-Curie, BP 146, F-13384 Marseille cedex 13, France
PATRICE MEUNIER
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, 49, rue F. Joliot-Curie, BP 146, F-13384 Marseille cedex 13, France
STÉPHANE LE DIZÈS
Affiliation:
Institut de Recherche sur les Phénomènes Hors Équilibre, 49, rue F. Joliot-Curie, BP 146, F-13384 Marseille cedex 13, France
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Abstract

This experimental and theoretical study considers the dynamics and the instability of a Lamb–Oseen vortex in a stably stratified fluid. In a companion paper, it was shown that tilting the vortex axis with respect to the direction of stratification induces the formation of a rim of strong axial flow near a critical radius when the Froude number of the vortex is larger than one.

Here, we demonstrate that this tilt-induced flow is responsible for a three-dimensional instability. We show that the instability results from a shear instability of the basic axial flow in the critical-layer region. The theoretical predictions for the wavelength and the growth rate obtained by a local stability analysis of the theoretical critical-layer profile are compared to experimental measurements and a good agreement is observed. The late stages of the instability are also analysed experimentally. In particular, we show that the tilt-induced instability does not lead to the destruction of the vortex, but to a sudden decrease of its Froude number, through the turbulent diffusion of its core size, when the initial Froude number is close to 1. A movie is available with the online version of the paper.

JFM classification

Vortex Flows: Vortex instability Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 596 , 25 January 2008 , pp. 1 - 20
Copyright
Copyright © Cambridge University Press 2008

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Boulanger et al. supplementary movie

Movie 1. Shadowgraph visualization of the tilt-induced instability of a stratified vortex in a vertical longitudinal plane for a tilt angle of 0.07 rad. The experiment is performed in a Plexiglas tank filled with linearly stratified fluid. The vortex is created by rotating impulsively a flap in the fluid. The sequence is in real time and the field of view is approximately 10 cm by 10 cm. Reynolds number, Re = 640; Froude number, F = 2.7.

Download Boulanger et al. supplementary movie(Video)
Video 4.1 MB

Boulanger et al. supplementary movie

Movie 1. Shadowgraph visualization of the tilt-induced instability of a stratified vortex in a vertical longitudinal plane for a tilt angle of 0.07 rad. The experiment is performed in a Plexiglas tank filled with linearly stratified fluid. The vortex is created by rotating impulsively a flap in the fluid. The sequence is in real time and the field of view is approximately 10 cm by 10 cm. Reynolds number, Re = 640; Froude number, F = 2.7.

Download Boulanger et al. supplementary movie(Video)
Video 2.6 MB