Vortices in rotating and stratified flows: aspect ratio and sustainability

O. Aubert; M. Le Bars; P. Le Gal; P. S. Marcus

doi:10.1051/epjconf/20134605004

EPJ

Vortices in rotating and stratified flows: aspect ratio and sustainability

O. Aubert¹^a, M. Le Bars¹, P. Le Gal¹ and P. S. Marcus²

¹ Institut de Recherche sur les Phénomènes Hors Equilibre, UMR 7342, CNRS and Aix-Marseille Université, 49 rue F. Joliot Curie, 13384 Marseille, Cédex 13, France
² Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA

Abstract

In linear stratifications, vortices have a typical flat shape that appears to be not only a compromise between the rotation and the stratification of the background flow through their Coriolis parameter f and buoyancy frequency $\hbox{$\bar{N}$}$ , but also involves the buoyancy frequency N_c within the vortices and their Rossby number R_o. We derive an analytical solution for the self-similar ellipsoidal shape of the vortices and the law for their aspect ratio. From this law, we show that long-lived vortices must necessary be either weakly stratified anticyclones or superstratified cyclones (which is less likely to occur). These predictions are experimentally and numerically verified and agree with published measurements for Jovian vortices and ocean meddies. This approach can be applied to a gaussian stratification to give good insights of the shape of vortices in protoplanetary disks and their sustainability.

12 Internat. Congress of the Balkan Physical Union
July 8-12, 2025
Bucharest, Romania

EPJ

Vortices in rotating and stratified flows: aspect ratio and sustainability

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