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Inertial instability in rotating and stratified fluids: barotropic vortices

Published online by Cambridge University Press:  04 July 2007

R. C. KLOOSTERZIEL ,
G. F. CARNEVALE  and
P. ORLANDI
R. C. KLOOSTERZIEL
Affiliation:
1School of Ocean & Earth Science & Technology, University of Hawaii, Honolulu, HI 96822, USA
G. F. CARNEVALE
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
P. ORLANDI
Affiliation:
Dipartimento di Meccanica e Aeronautica, University of Rome, “La Sapienza,” via Eudossiana 18, 00184 Roma, Italy
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Abstract

The unfolding of inertial instability in intially barotropic vortices in a uniformly rotating and stratified fluid is studied through numerical simulations. The vortex dynamics during the instability is examined in detail. We demonstrate that the instability is stabilized via redistribution of angular momentum in a way that produces a new equilibrated barotropic vortex with a stable velocity profile. Based on extrapolations from the results of a series of simulations in which the Reynolds number and strength of stratification are varied, we arrive at a construction based on angular momentum mixing that predicts the infinite-Reynolds-number form of the equilibrated vortex toward which inertial instability drives an unstable vortex. The essential constraint is conservation of total absolute angular momentum. The construction can be used to predict the total energy loss during the equilibration process. It also shows that the equilibration process can result in anticyclones that are more susceptible to horizontal shear instabilities than they were initially, a phenomenon previously observed in laboratory and numerical studies.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 379 - 412
Copyright
Copyright © Cambridge University Press 2007

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References

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