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Tilt-induced instability of a stratified vortex
Published online by Cambridge University Press: 17 January 2008
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.
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References
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.
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.
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