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On the dynamics of finite-amplitude baroclinic waves as a function of supercriticality

Published online by Cambridge University Press:  11 April 2006

Joseph Pedlosky
Joseph Pedlosky
Affiliation:
Department of the Geophysical Sciences, University of Chicago, Illinois 60637
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Abstract

A finite-amplitude model of baroclinic instability is studied in the case where the cross-stream scale is large compared with the Rossby deformation radius and the dissipative and advective time scales are of the same order. A theory is developed that describes the nature of the wave field as the shear supercriticality increases beyond the stability threshold of the most unstable cross-stream mode and penetrates regions of higher supercriticality. The set of possible steady nonlinear modes is found analytically. It is shown that the steady cross-stream structure of each finite-amplitude mode is a function of the supercriticality.

Integrations of initial-value problems show, in each case, that the final state realized is the state characterized by the finite-amplitude mode with the largest equilibrium amplitude. The approach to this steady state is oscillatory (nonmonotonic). Further, each steady-state mode is a well-defined mixture of linear cross-stream modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 78 , Issue 3 , 7 December 1976 , pp. 621 - 637
Copyright
© 1976 Cambridge University Press

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References

Byrd, P. F. & Friedman, M. D. 1971 Handbook of Elliptic Integrals for Engineers and Scientists. Springer.
Drazin, P. G. 1970 Non-linear baroclinic instability of a continuous zonal flow. Quart. J. Roy. Met. Soc. 96, 667–676.Google Scholar
Hart, J. E. 1973 On the behavior of large-amplitude baroclinic waves. J. Atmos. Sci. 30, 1017–1034.Google Scholar
Lorenz, E. N. 1963 The mechanics of vacillation. J. Atmos. Sci. 20, 448–464.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
Pedlosky, J. 1972 Limit cycles and unstable baroclinic waves. J. Atmos. Sci. 29, 53–63.Google Scholar
Phillips, N. A. 1951 A simple three-dimensional model for the study of large scale extra tropical flow pattern. J. Met. 8, 381–394.Google Scholar