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Nonlinear internal gravity waves in a rotating fluid

Published online by Cambridge University Press:  29 March 2006

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

The interaction between internal gravity waves in a rotating frame and the mean flow is discussed for the case when the properties of the mean flow vary slowly on a scale determined by the local wave structure. The principle of conservation of wave action is established. It is shown that the main effect of the waves on the Lagrangian mean velocity is due to an appropriate ‘radiation stress’ tensor. A circulation theorem and a potential-vorticity equation are derived for the mean velocity.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 71 , Issue 3 , 14 October 1975 , pp. 497 - 512
Copyright
© 1975 Cambridge University Press

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References

Bretherton, F. P. 1969 J. Fluid Mech. 36, 785–803.
Bretherton, F. P. 1971 The general linearised theory of wave propagation. In Mathematical Problems in the Geophysical Sciences, vol. 1. Geophysical Fluid Dynamics, Lectures in Applied Mathematics, vol. 13, pp. 61–102. Am. Math. Soc.
Bretherton, F. P. & Garrett, C. J. R. 1969 Proc. Roy. Soc. A 302, 529–554.
Garrett, C. J. R. 1968 J. Fluid Mech. 34. 711–720.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Grimshaw, R. 1972 J. Fluid Mech. 54, 193–207.
Grimshaw, R. 1974 Geophys. Fluid Dyn. 6, 131–148.
Grimshaw, R. 1975a Tellus (to be published).
Grimshaw, R. 1975b J. Fluid Mech. 70, 287–304.
Mcintyre, M. E. 1973 J. Fluid Mech. 60, 801–811.
Pedlosky, J. 1971 Geophysical fluid dynamics. In Mathematical Problems in the Geophysical Sciences, vol. 1. Geophysical Fluid Dynamics, Lectures in Applied Mathematics, vol. 13, pp. 1–60. Am. Math. Soc.
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.