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On the mean motion induced by internal gravity waves

Published online by Cambridge University Press:  29 March 2006

Francis P. Bretherton
Francis P. Bretherton
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla
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Abstract

A train of internal gravity waves in a stratified liquid exerts a stress on the liquid and induces changes in the mean motion of second order in the wave amplitude. In those circumstances in which the concept of a slowly varying quasi-sinusoidal wave train is consistent, the mean velocity is almost horizontal and is determined to a first approximation irrespective of the vertical forces exerted by the waves. The sum of the mean flow kinetic energy and the wave energy is then conserved. The circulation around a horizontal circuit moving with the mean velocity is increased in the presence of waves according to a simple formula. The flow pattern is obtained around two- and three-dimensional wave packets propagating into a liquid at rest and the results are generalized for any basic state of motion in which the internal Froude number is small. Momentum can be associated with a wave packet equal to the horizontal wave-number times the wave energy divided by the intrinsic frequency.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 36 , Issue 4 , 19 May 1969 , pp. 785 - 803
Copyright
© 1969 Cambridge University Press

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