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Over-reflection of internal-inertial waves from the mixed layer

Published online by Cambridge University Press:  20 April 2006

M. Kamachi  and
R. Grimshaw
M. Kamachi
Affiliation:
Research Institute for Applied Mechanics, Kyushu University 87, Kasuga-city, Fukuoka, 816, Japan
R. Grimshaw
Affiliation:
Department of Mathematics, University of Melbourne, Parkville, Victoria 3052, Australia
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Abstract

Near-inertial oscillations associated with downward energy propagation are commonly observed in the upper ocean. Stern (1977) has suggested that these observations may be internal-inertial waves over-reflected from the shear zone at the base of the mixed layer. In this paper we develop a criterion for over-reflection as a function of wavenumber and frequency for a class of shear flows in the mixed layer. By examining the vertical profile of the vertical wave action flux we demonstrate that the source of the over-reflection is the shear at the base of the mixed layer, which is maintained by the wind-induced turbulent Reynolds stress, here parametrized as a body force. The relationship between over-reflection and the wave-induced Lagrangian-mean flow is determined. We also determine a criterion for unstable waves, and show that these are contiguous in wavenumber-frequency space with points of resonant over-reflection. However, the growth rates of these unstable waves are quite small, and in practice unstable waves will be indistinguishable from waves generated by over-reflection.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 141 , April 1984 , pp. 179 - 196
Copyright
© 1984 Cambridge University Press

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