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Saturation of inertial instability in rotating planar shear flows

Published online by Cambridge University Press:  04 July 2007

R. C. KLOOSTERZIEL ,
P. ORLANDI  and
G. F. CARNEVALE
R. C. KLOOSTERZIEL
Affiliation:
School of Ocean & Earth Science & 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
G. F. CARNEVALE
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093, USA
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Abstract

Inertial instability in a rotating shear flow redistributes absolute linear momentum in such a way as to neutralize the instability. In the absence of other instabilities, the final equilibrium can be predicted by a simple construction based on conservation of total momentum. Numerical simulations, invariant in the along-stream direction, suppress barotropic instability and allow only inertial instability to develop. Such simulations, at high Reynolds numbers, are used to test the theoretical prediction. Four representative examples are given: a jet, a wall-bounded jet, a mixing layer and a wall-bounded shear layer.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 583 , 25 July 2007 , pp. 413 - 422
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Afanasyev, Y. D. & Peltier, W. R. 1998 Three-dimensional instability of anticyclonic flow in a rotating fluid: Laboratory experiments and related theoretical predictions. Phys. Fluids 10, 3194–3202.CrossRefGoogle Scholar
Charney, J. G. 1973 Lecture notes on planetary fluid dynamics. In Dynamic Meteorology (Morel, ed. P.). Reidel.Google Scholar
Griffiths, S. D. 2003a The nonlinear evolution of zonally symmetric equatorial inertial instability. J. Fluid Mech. 474 245–273.CrossRefGoogle Scholar
Griffiths, S. D. 2003b Nonlinear vertical scale selection in equatorial inertial instability. J. Atmos. Sci. 60, 977–990.2.0.CO;2>CrossRefGoogle Scholar
Holton, J. R. 1992 An Introduction to Dynamic Meteorology. Academic Press.Google Scholar
Kloosterziel, R. C., Carnevale, G. F. & Orlandi, P. 2007 Inertial instability in rotating and stratified fluids: barotropic vortices. J. Fluid Mech. 583, 379–412.CrossRefGoogle Scholar
Ooyama, K. 1966 On the stability of the baroclinic circular vortex: a sufficient condition for instability. J. Atmos. Sci. 23, 43–53.2.0.CO;2>CrossRefGoogle Scholar
Orlandi, P. 2000 Fluid Flow Phenomena: A Numerical Toolkit. Kluwer.CrossRefGoogle Scholar
Shen, C. Y. & Evans, T. E. 1998 Inertial instability of large Rossby number horizontal shear flows in a thin homogeneous layer. Dyn. Atmos. Oceans 26, 185–208.CrossRefGoogle Scholar
Shen, C. Y. & Evans, T. E. 2002 Inertial instability and sea spirals. Geophys. Res. Lett. 29, 21–24.CrossRefGoogle Scholar