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Nonlinear baroclinic instability of a continuous zonal flow of viscous fluid

Published online by Cambridge University Press:  29 March 2006

P. G. Drazin
P. G. Drazin
Affiliation:
School of Mathematics, University of Bristol
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Abstract

Nonlinear instability of a zonal flow of slightly viscous Boussinesq fluid in a rapidly rotating frame is studied mathematically by the method of normal mode cascade, the flow being along a rectangular channel with horizontal and vertical rigid walls. Viscosity is represented approximately by supposing that its only effects occur in Ekman layers near the top and bottom walls of the channel, after the linear model of Barcilon. Self-interaction of one slightly unstable mode is found to lead to equilibration with supercritical instability. Also, interactions of two slightly unstable modes plausibly lead to equilibration. These results are related to the literature of experiments on differentially heated, rotating annuli.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 4 , 24 October 1972 , pp. 577 - 587
Copyright
© 1972 Cambridge University Press

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References

Barcilon, V. 1964 Role of the Ekman layers in the stability of the symmetric regime obtained in a rotating annulus. J. Atmos. Sci. 21, 291–299.Google Scholar
Drazin, P. G. 1970 Non-linear baroclinic instability of a continuous zonal flow. Quart. J. Roy. Met. Soc. 96, 667–676.Google Scholar
Fowlis, W. W. & Hide, R. 1965 Thermal convection in a rotating annulus: effect of viscosity on the transition between axisymmetric and non-axisymmetric flow regimes. J. Atmos. Sci. 22, 541–558.Google Scholar
Hide, R. 1970 Some laboratory experiments on free thermal convection in a rotating fluid subject to horizontal temperature gradient and their relation to the theory of global atmospheric circulation. In The Global Circulation of the Atmosphere (ed. G. A. Corby), pp. 196–221. London: Roy. Met. Soc.
Kaiser, J. A. C. 1970 Rotating deep annulus convection. Part 2. Wave instabilities, vertical stratification, and associated theories. Tellus, 22, 275–287.Google Scholar
Pedlosky, J. 1970 Finite-amplitude baroclinic waves. J. Atmos. Sci. 27, 15–30.Google Scholar
Pedlosky, J. 1971 Finite-amplitude baroclinic waves with small dissipation. J. Atmos. Sci. 28, 587–597.Google Scholar
Segel, L. A. 1966 Nonlinear hydrodynamic stability theory and its application to thermal convection and curved flows. In Non-equilibrium Thermodynamics, Variational Techniques and Stability (ed. R. J. Donnelly, I. Prigogine & R. Herman), pp. 165–197. University of Chicago Press.
Segel, L. A. & Stuart, J. T. 1962 On the question of the preferred mode in cellular thermal convection. J. Fluid Mech. 13, 289–306.Google Scholar