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Vertical scale selection in inertial instability†

Published online by Cambridge University Press:  14 December 2007

R. C. KLOOSTERZIEL  and
G. F. CARNEVALE
R. C. KLOOSTERZIEL
Affiliation:
School 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
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Abstract

The linear instability of a barotropic flow with uniform horizontal shear in a stratified rotating fluid is investigated with respect to perturbations invariant in the alongflow direction. The flow can be inertially unstable if there is sufficiently strong anticyclonic shear, but only for sufficiently high Reynolds numbers Re. We determine the critical Reynolds numbers required for amplification of the instability as a function of Prandtl number, strength of the stratification and magnitude of the shear. The vertical scales at the onset of the instability are calculated. For Prandtl number P < 1.44 instability always sets in through stationary overturning motions, for P > 1.44 it may also commence through overstable (oscillatory) motions. For Re exceeding the critical value, we determine the vertical scale of the most rapidly amplifying modes and the corresponding growth rates and how they vary with Re, P, the shear and the strength of stratification.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 594 , 10 January 2008 , pp. 249 - 269
Copyright
Copyright © Cambridge University Press 2008

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Footnotes

†

With an appendix by Stephen D. Griffiths

References

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