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On internal gravity waves in an accelerating shear flow

Published online by Cambridge University Press:  19 April 2006

S. A. Thorpe
S. A. Thorpe
Affiliation:
Institute of Oceanographic Sciences, Wormley, Godalming, Surrey, England
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Abstract

The investigation of the effects which a changing mean flow has on a uniform train of internal gravity waves (Thorpe 1978a) is continued by considering waves in a uniformly accelerating stratified plane Couette flow with constant density gradient. Experiments reveal a change in the mode structure and phase distribution of the waves, and their eventual breaking near the boundary where the mean flow is greatest, the phase speed of the waves being positive. A linear numerical model is devised which accurately describes the waves up to the onset of their breaking, and this is used to investigate their energetics. The working of the Reynolds stress against the mean velocity gradient results in a very rapid transfer of energy from the waves to the mean flow, so that by the time breaking occurs only a small fraction of their initial energy remains for possible transfer into potential energy of the fluid.

The consequences have important applications in oceanography and meteorology, to flow stability and flow generation, and explain some earlier laboratory observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 4 , 27 October 1978 , pp. 623 - 639
Copyright
© 1978 Cambridge University Press

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References

Banks, W. H. H., Dbazin, P. G. & Zaturska, M. B. 1976 On the normal modes of parallel flow of inviscid stratified fluid. J. Fluid Mech. 75, 149–171.Google Scholar
Davey, A. & Reid, W. H. 1977 On the stability of stratified viscous plane Couette flow. Part 1. Constant buoyancy frequency. J. Fluid Mech. 80, 509–526.Google Scholar
Eliassen, A., HøILAND, E. & Riis, E. 1953 Two-dimensional perturbation of a flow with constant shear of a stratified fluid. Inst. Weather Climate Res., Norwegian Acad. Sci. Lett. Publ. no. 1.Google Scholar
Goodman, J. K. & Miller, A. 1977 Mass transport across a density inversion. J. Geophys. Res. 82, 3463–3471.Google Scholar
Halpern, D. 1974 Observations of the deepening of the wind mixed layer in the Northeast Pacific Ocean. J. Phys. Ocean. 4, 454–466.Google Scholar
Habtman, R. J. 1975 Wave propagation in a stratified shear flow. J. Fluid Mech. 71, 89–104.Google Scholar
Holton, J. R. & Lindzen, R. S. 1972 An updated theory for the quasi-biennial oscillation of the tropical stratosphere. J. Atmos. Sci. 29, 1076–1080.Google Scholar
Kato, H. & Phillips, O. M. 1969 On the penetration of a turbulent layer into stratified fluid. J. Fluid Mech. 37, 643–655.Google Scholar
Mcewan, A. D. & Robinson, R. M. 1975 Parametric instability of internal gravity waves. J. Fluid Mech. 67, 667–688.Google Scholar
Phillips, O. M. 1966 The Dynamics of the Upper Ocean. Cambridge University Press.
Plumb, R. A. 1977 The interaction of two internal waves with the mean flow; implications for the theory of the quasi-biennial oscillation. J. Atmos. Sci. 34, 1847–1858.Google Scholar
Scorer, R. S. & Wilson, S. D. R. 1963 Secondary instability in steady gravity waves. Quart. J. Roy. Met. Soc. 89, 532–539.Google Scholar
Thorpe, S. A. 1968a On the shape of progressive internal waves. Phil. Trans. Roy. Soc. A 263, 563–614.Google Scholar
Thorpe, S. A. 1968b A method of producing a shear flow in a stratified fluid. J. Fluid Mech. 32, 693–704.Google Scholar
Thorpe, S. A. 1973 Experiments on instability and turbulence in a stratified shear flow. J. Fluid Mech. 61, 731–751.Google Scholar
Thorpe, S. A. 1978a On the shape and breaking of finite amplitude internal gravity waves in a shear flow. J. Fluid Mech. 85, 7–31.Google Scholar
Thorpe, S. A. 1978b The near-surface ocean mixing layer in stable heating conditions. J. Geophys. Res. 83, 2875–2885.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.