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The universal aspect ratio of vortices in rotating stratified flows: experiments and observations

Published online by Cambridge University Press:  25 May 2012

Oriane Aubert
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 7342, CNRS and Aix-Marseille Université, 49 rue F. Joliot Curie, 13384 Marseille, CEDEX 13, France
Michael Le Bars
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 7342, CNRS and Aix-Marseille Université, 49 rue F. Joliot Curie, 13384 Marseille, CEDEX 13, France
Patrice Le Gal
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 7342, CNRS and Aix-Marseille Université, 49 rue F. Joliot Curie, 13384 Marseille, CEDEX 13, France
Philip S. Marcus
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
Corresponding
E-mail address:

Abstract

We validate a new law for the aspect ratio of vortices in a rotating, stratified flow, where and are the vertical half-height and horizontal length scale of the vortices. The aspect ratio depends not only on the Coriolis parameter and buoyancy (or Brunt–Väisälä) frequency of the background flow, but also on the buoyancy frequency within the vortex and on the Rossby number of the vortex, such that . This law for is obeyed precisely by the exact equilibrium solution of the inviscid Boussinesq equations that we show to be a useful model of our laboratory vortices. The law is valid for both cyclones and anticyclones. Our anticyclones are generated by injecting fluid into a rotating tank filled with linearly stratified salt water. In one set of experiments, the vortices viscously decay while obeying our law for , which decreases over time. In a second set of experiments, the vortices are sustained by a slow continuous injection. They evolve more slowly and have larger while still obeying our law for . The law for is not only validated by our experiments, but is also shown to be consistent with observations of the aspect ratios of Atlantic meddies and Jupiter’s Great Red Spot and Oval BA. The relationship for is derived and examined numerically in a companion paper by Hassanzadeh, Marcus & Le Gal (J. Fluid Mech., vol. 706, 2012, pp. 46–57).

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Copyright © Cambridge University Press 2012

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References

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