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Internal-wave interactions in the induced-diffusion approximation

Published online by Cambridge University Press:  20 April 2006

James D. Meiss  and
Kenneth M. Watson
James D. Meiss
Affiliation:
Department of Physics, University of California, Berkeley Present address: Institute for Fusion Studies, University of Texas, Austin, Texas
Kenneth M. Watson
Affiliation:
Center for Studies of Nonlinear Dynamics, La Jolla Institute, P.O. Box 1434, La Jolla, CA 92038 Present Address: Marine Physical Laboratory of the Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093
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Abstract

Dynamical equations for the interaction of high-wavenumber, high-frequency internal waves with a prescribed, linear, large-scale internal-wave field are obtained from the Boussinesq–Euler equations. The relationship of these ‘induced-diffusion’ interactions to the Taylor–Goldstein equation is discussed. Exact equations are derived in the induced-diffusion limit of McComas & Bretherton (1977) for the evolution of the first and second moments of the small-scale flow when the large-scale flow is assumed random. Estimates of corrections to the induced-diffusion approximation for the Garrett–Munk internal-wave model indicate the domain of applicability of these equations. Computations of the autocorrelation function and action transport in wavenumber and physical space are presented. Severe limitations are found on the applicability of two-time perturbation theory and the resonant-interaction approximation. The high transfer rates found by McComas & Bretherton in the induceddiffusion regime are reduced significantly in the present calculations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 117 , April 1982 , pp. 315 - 341
Copyright
© 1982 Cambridge University Press

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