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Forced resonant second-order interaction between damped internal waves

Published online by Cambridge University Press:  29 March 2006

A. D. Mcewan ,
D. W. Mander  and
R. K. Smith
A. D. Mcewan
Affiliation:
C.S.I.R.O. Division of Atmospheric Physics, Aspendale, Victoria, Australia
D. W. Mander
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria, Australia
R. K. Smith
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria, Australia Present address: Department of Applied Mathematics, University of Edinburgh.
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Abstract

A theoretical and experimental study is made of the second-order resonant interaction between triads of linearly damped waves, one common member of which is continuously forced. In the case of a single triad, if the forced wave exceeds a critical amplitude defined by properties of the triad members, energy proceeds irreversibly to the other two waves. A stable limit state is reached where all power in excess of that required to sustain a critical amplitude in the forced wave is transferred to the other waves, which also reach steady terminal amplitudes.

It is shown that when two or more triads are simultaneously at resonance the only stable limit state is one wherein the forced wave has fallen to the lowest critical amplitude, and the only other two waves remaining are those of the triad possessing this critical amplitude. Regardless of their initial amplitudes, all other waves not externally forced ultimately disappear.

The theory is applied to the interaction of standing internal gravity waves in a linearly stratified liquid. The experiments described here quantitatively confirm the major predictions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 55 , Issue 4 , 24 October 1972 , pp. 589 - 608
Copyright
© 1972 Cambridge University Press

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