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Stochastic closure for nonlinear Rossby waves

Published online by Cambridge University Press:  12 April 2006

Greg Holloway  and
Myrl C. Hendershott
Greg Holloway
Affiliation:
Scripps Institution of Oceanography, La Jolla, California 92037 Present address: National Center for Atmospheric Research, Advanced Study Program, P.O. Box 3000, Boulder, Colorado 80307.
Myrl C. Hendershott
Affiliation:
Scripps Institution of Oceanography, La Jolla, California 92037
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Abstract

An extension of the turbulence ‘test-field model’ (Kraichnan 1971 a) is given for two-dimensional flow with Rossby-wave propagation. Such a unified treatment of waves and turbulence is necessary for flows in which the relative strength of nonlinear terms depends upon the length scale considered. We treat the geophysically interesting case in which long, fast Rossby waves propagate substantially without interaction while short Rossby waves are thoroughly dominated by advection. We recover the observations of Rhines (1975) that the tendency of two-dimensional flow to organize energy into larger scales of motion is inhibited by Rossby waves and that an initially isotropic flow develops anisotropy preferring zonal motion. The anisotropy evolves to an equilibrium functional dependence on the isotropic part of the flow spectrum. Theoretical results are found to be in quantitative agreement with numerical flow simulations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 4 , 14 October 1977 , pp. 747 - 765
Copyright
© 1977 Cambridge University Press

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