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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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