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The effect of dissipative processes on mean flows induced by internal gravity-wave packets

Published online by Cambridge University Press:  20 April 2006

R. Grimshaw
R. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
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Abstract

Grimshaw (1979) discussed the mean flow induced by an internal gravity-wave packet propagating in a shear flow. The present paper analyses the effect of dissipative processes on this problem. In a manner similar to that described by Longuet-Higgins (1953) for water waves, frictional effects in the Stokes boundary layers modify the mean-flow field just outside the boundary layers. Just outside the bottom boundary layer there is a wave-induced mean Lagrangian velocity, whose magnitude is proportional to the square of the wave amplitude, while just below the free-surface boundary layer there is a wave-induced mean-velocity gradient. In the interior of the fluid the presence of dissipation in the wave field will induce a significant mean-flow field whenever the group velocity of the wave packet exceeds the phase speed of a longwave mode. Ultimately, this interior mean flow will be modified by diffusion from the boundaries of effects induced in the aforementioned Stokes layers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 347 - 377
Copyright
© 1982 Cambridge University Press

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