https://doi.org/10.1051/epjconf/20134605004
Vortices in rotating and stratified flows: aspect ratio and sustainability
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
a e-mail: aubert@irphe.univ-mrs.fr
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 
, but also involves the buoyancy frequency
Nc within the vortices and their Rossby
number Ro. 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.
© Owned by the authors, published by EDP Sciences, 2013
