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On the formation of geophysical and planetary zonal flows by near-resonant wave interactions

Published online by Cambridge University Press:  28 March 2007

YOUNGSUK LEE  and
LESLIE M. SMITH
YOUNGSUK LEE
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada
LESLIE M. SMITH
Affiliation:
Departments of Mathematics and Engineering Physics, University of Wisconsin, Madison, WI 53706, USA
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Abstract

Numerical simulations on a β-plane are used to further understand the formation of zonal flows from small-scale fluctuations. The dynamics of ‘reduced models’ are computed by restricting the nonlinear term to include a subset of triad interactions in Fourier space. Reduced models of near-resonant triads are considered, as well as the complement set of non-resonant triads. At moderately small values of the Rhines number, near-resonant triad interactions are shown to be responsible for the generation of large-scale zonal flows from small-scale random forcing. Without large-scale drag, both the full system and the reduced model of near resonances produce asymmetry between eastward and westward jets, in favour of stronger westward jets. When large-scale drag is included, the long-time asymmetry is reversed in the full system, with eastward jets that are thinner and stronger than westward jets. Then the reduced model of near resonances exhibits a weaker asymmetry, but there are nevertheless more eastward jets stronger than a threshold value.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 576 , 10 April 2007 , pp. 405 - 424
Copyright
Copyright © Cambridge University Press 2007

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