Journal of Fluid Mechanics

Papers

Tilt-induced instability of a stratified vortex

NICOLAS BOULANGERa1, PATRICE MEUNIERa1 and STÉPHANE LE DIZÈSa1

a1 Institut de Recherche sur les Phénomènes Hors Équilibre, 49, rue F. Joliot-Curie, BP 146, F-13384 Marseille cedex 13, France

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.

(Received April 24 2007)

(Revised August 31 2007)

Key words

  • Vortex instability;
  • Stratified flows
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