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Inertial and barotropic instabilities of a free current in three-dimensional rotating flow

Published online by Cambridge University Press:  14 May 2013

G. F. Carnevale ,
R. C. Kloosterziel  and
P. Orlandi
G. F. Carnevale*
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
R. C. Kloosterziel
Affiliation:
School of Ocean and Earth Science and Technology, University of Hawaii, Honolulu, HI 96822, USA
P. Orlandi
Affiliation:
Dipartimento di Meccanica e Aeronautica, University of Rome, ‘La Sapienza’, via Eudossiana 18, 00184 Roma, Italy
*
†Email address for correspondence: [email protected]
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Abstract

A current in a homogeneous rotating fluid is subject to simultaneous inertial and barotropic instabilities. Inertial instability causes rapid mixing of streamwise absolute linear momentum and alters the vertically averaged velocity profile of the current. The resulting profile can be predicted by a construction based on absolute-momentum conservation. The alteration of the mean velocity profile strongly affects how barotropic instability will subsequently change the flow. If a current with a symmetric distribution of cyclonic and anticyclonic vorticity undergoes only barotropic instability, the result will be cyclones and anticyclones of the same shape and amplitude. Inertial instability breaks this symmetry. The combined effect of inertial and barotropic instability produces anticyclones that are broader and weaker than the cyclones. A two-step scheme for predicting the result of the combined inertial and barotropic instabilities is proposed and tested. This scheme uses the construction for the redistribution of streamwise absolute linear momentum to predict the mean current that results from inertial instability and then uses this equilibrated current as the initial condition for a two-dimensional simulation that predicts the result of the subsequent barotropic instability. Predictions are made for the evolution of a Gaussian jet and are compared with three-dimensional simulations for a range of Rossby numbers. It is demonstrated that the actual redistribution of absolute momentum in the three-dimensional simulations is well predicted by the construction used here. Predictions are also made for the final number and size of vortices that result from the combined inertial and barotropic instabilities.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Instability: Instability Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 725 , 25 June 2013 , pp. 117 - 151
Copyright
©2013 Cambridge University Press 

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