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Estimating intermittency in three-dimensional Navier–Stokes turbulence

Published online by Cambridge University Press:  14 April 2009

J. D. GIBBON
J. D. GIBBON*
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
*
†E-mail address for correspondence: j.d.gibbon@ic.ac.uk
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Abstract

The issue of why computational resolution in Navier–Stokes turbulence is hard to achieve is addressed. Under the assumption that the three-dimensional Navier–Stokes equations have a global attractor it is nevertheless shown that solutions can potentially behave differently in two distinct regions of space–time ± where − is comprised of a union of disjoint space–time ‘anomalies’. If − is non-empty it is dominated by large values of |∇ω|, which is consistent with the formation of vortex sheets or tightly coiled filaments. The local number of degrees of freedom ± needed to resolve the regions in ± satisfies , where u = uL/ν is a Reynolds number dependent on the local velocity field u(x, t).

Type
Papers
Information
Journal of Fluid Mechanics , Volume 625 , 25 April 2009 , pp. 125 - 133
Copyright
Copyright © Cambridge University Press 2009

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