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Long nonlinear waves in stratified shear flows

Published online by Cambridge University Press:  19 April 2006

S. A. Maslowe  and
L. G. Redekopp
S. A. Maslowe
Affiliation:
Mathematics Department, McGill University, Montreal, P.Q. H3A 2K6
L. G. Redekopp
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, California 90007
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Abstract

The propagation of finite-amplitude internal waves in a shear flow is considered for wavelengths that are long compared to the shear-layer thickness. Both singular and regular modes are investigated, and the equation governing the amplitude evolution is derived. The theory is generalized to allow for a radiation condition when the region outside the stratified shear layer is unbounded and weakly stratified. In this case, the evolution equation contains a damping term describing energy loss by radiation which can be used to estimate the persistence of solitary waves or nonlinear wave packets in realistic environments. A continuous three-layer model is studied in detail and closed-form expressions are obtained for the phase speed and the coefficients of the nonlinear and dispersive terms in the amplitude equation as a function of Richardson number.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 101 , Issue 2 , 27 November 1980 , pp. 321 - 348
Copyright
© 1980 Cambridge University Press

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