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Degeneration of resonantly-excited standing internal gravity waves

Published online by Cambridge University Press:  29 March 2006

A. D. McEwan
A. D. McEwan
Affiliation:
C.S.I.R.O., Division of Meteorological Physics, Aspendale, Victoria, 3195 Australia
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Abstract

The factors bringing about the irreversible distortion or degeneration of a continuously forced standing internal gravity wave in a linearly stratified fluid are studied experimentally and theoretically. For a rectangular container there is strong evidence that the process is initiated by the unstable growth, from a subliminal level, of free wave modes forming triads in second-order resonant interaction with the original wave. These free modes grow by de-energizing the original wave and may collectively induce kinematical conditions sufficiently severe to create localized regions of density discontinuity within the fluid, leading to turbulence.

Although the possible free wave modes are doubly infinite in number, the geometrical constraints greatly reduce the number of possibilities for resonant triads. In many cases this permits critical wave amplitude to be predicted by consideration of one triad only, and the results are in excellent agreement with experiment.

It is speculated that a closely similar process explains observations by Malkus (1968), Aldridge & Toomre (1969), and McEwan (1970) in the analogous context of inertial oscillation of contained rotating fluids.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 50 , Issue 3 , 14 December 1971 , pp. 431 - 448
Copyright
© 1971 Cambridge University Press

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References

Aldridge, K. D. & Toomre, A. 1969 J. Fluid Mech. 37, 307.
Baines, P. G. 1967 J. Fluid Mech. 30, 533.
Benjamin, T. B. & Fier, J. E. 1967 J. Fluid Mech. 27, 417.
Craik, A. D. D. 1968 J. Fluid Mech. 34, 531.
Davis, R. E. & Acrivos, A. 1967 J. Fluid Mech. 30, 723.
Hasselmann, K. 1967 J. Fluid Mech. 30, 737.
Hoerner, S. F. 1953 Fluid Dynamic Drag. Hoerner.
Malkus, W. V. R. 1968 Science, 160, 259.
Martin, S., Simmons, W. F. & Wunsch, C. I. 1969 Nature, 224, 1014.
Mcewan, A. D. 1970 J. Fluid Mech. 40, 603.
Mcgoldrick, L. F. 1970 J. Fluid Mech. 40, 251.
Oster, G. 1965 Scient. Amer. 213, 70.
Taylor, G. I. 1953 Proc. Roy. Soc. A 218, 44.
Thorpe, S. A. 1966 J. Fluid Mech. 24, 737.
Thorpe, S. A. 1968 J. Fluid Mech. 32, 489.