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On the generation of large-scale structures in a homogeneous eddy field

Published online by Cambridge University Press:  16 November 2010

TIMOUR RADKO
TIMOUR RADKO*
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 9394, USA
*
†Email address for correspondence: tradko@nps.edu
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Abstract

An analytical theory is developed which illustrates dynamics of the spontaneous generation of large-scale structures in the unforced two-dimensional eddying flows. The eddy field is represented by the closely packed array of standing coherent vortices whose intensity is weakly modulated by the long-wavelength perturbations introduced into the system. The asymptotic multiscale analysis makes it possible to identify instabilities resulting from the positive feedback of the background eddies on large-scale perturbations. Initially, these instabilities amplify at a rate proportional to the square root of their wavenumber. Linear growth is arrested when the amplitude of the long-wavelength perturbations reaches the level of background eddies. The subsequent evolutionary pattern is characterized by the emergence of relatively sharp features in the large-scale streamfunction field – features suggestive of the coherent jets commonly observed in eddying geophysical flows. The proposed solutions differ substantially from their counterparts in forced-dissipative systems, exemplified by the canonical model of Kolmogorov flow. The asymptotic model is successfully tested against numerical simulations.

JFM classification

Instability: Instability Geophysical and Geological Flows: Ocean processes Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 76 - 99
Copyright
Copyright © Cambridge University Press 2010

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