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Rossby wave interaction in a shear flow with critical levels

Published online by Cambridge University Press:  26 April 2006

Jacques Vanneste
Jacques Vanneste
Affiliation:
Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
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Abstract

An approach is presented for studying Rossby wave interaction in a shear flow with both regular and singular modes (i.e. those possessing a critical level). The approach relies on a truncated normal mode expansion of the equations of motion. Such an expansion remains valid in the presence of singular modes, provided that these modes are not considered individually, but that complete packets are taken into account in the truncated system. Mathematically, this means that the interaction equations need to be integrated with respect to the phase velocity (or, equivalently, the critical level position) of the singular modes.

The action of two regular modes on a packet of singular modes is treated in detail; in particular, asymptotic results are deduced for the long-term behaviour of the packet. The case of a linear shear is considered as an illustration: analytical expressions are derived for the normal modes and their pseudomomentum, and they are used to present explicit results for the evolution of the packet of singular modes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 323 , 25 September 1996 , pp. 317 - 338
Copyright
© 1996 Cambridge University Press

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