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

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.

Type
Papers
Copyright
Copyright © Cambridge University Press 2010

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