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The interaction of long and short internal gravity waves: theory and experiment

Published online by Cambridge University Press:  20 April 2006

C. G. Koop  and
L. G. Redekopp
C. G. Koop
Affiliation:
Fluid Mechanics Department, TRW Systems, One Space Park, Redondo Beach, CA 90278
L. G. Redekopp
Affiliation:
Fluid Mechanics Department, TRW Systems, One Space Park, Redondo Beach, CA 90278 Permanent address: Department of Aerospace Engineering, University of Southern California, Los Angeles.
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Abstract

An analysis is presented which describes the slow-time evolution of an internal gravity wave in an arbitrarily specified stratification. The weakly nonlinear description of a single-wave mode, governed by the nonlinear Schrödinger equation, breaks down when certain resonant conditions are satisfied. One such condition occurs when the group velocity of the wavetrain is equal to the phase velocity of a higher-mode long wave of the system. The resonant interaction occurs on a faster time scale and is described by a coupled pair of nonlinear partial differential equations governing the evolution of both the short-wave and the long-wave modes. This long-wave/short-wave interaction is pursued further in an experimental investigation by measuring the modal interchange of energy between two internal waves of disparate length and time scales. The resulting data are compared with numerical solutions of the long-wave/short-wave resonant interaction equations. In general, the agreement between the theory and the experiment is reasonably good in the range of operating conditions for which the theory is valid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 111 , October 1981 , pp. 367 - 409
Copyright
© 1981 Cambridge University Press

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