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Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture

Published online by Cambridge University Press:  29 March 2011

SERGEI V. NAZARENKO  and
ALEXANDER A. SCHEKOCHIHIN
SERGEI V. NAZARENKO
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK Institut Henri Poincaré, Université Pierre et Marie Curie, 75231 Paris CEDEX 5, France
ALEXANDER A. SCHEKOCHIHIN*
Affiliation:
Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK Institut Henri Poincaré, Université Pierre et Marie Curie, 75231 Paris CEDEX 5, France
*
†Email address for correspondence: a.schekochihin1@physics.ox.ac.uk
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Abstract

It is proposed that critical balance – a scale-by-scale balance between the linear propagation and nonlinear interaction time scales – can be used as a universal scaling conjecture for determining the spectra of strong turbulence in anisotropic wave systems. Magnetohydrodynamic (MHD), rotating and stratified turbulence are considered under this assumption and, in particular, a novel and experimentally testable energy cascade scenario and a set of scalings of the spectra are proposed for low-Rossby-number rotating turbulence. It is argued that in neutral fluids the critically balanced anisotropic cascade provides a natural path from strong anisotropy at large scales to isotropic Kolmogorov turbulence at very small scales. It is also argued that the k−2⊥ spectra seen in recent numerical simulations of low-Rossby-number rotating turbulence may be analogous to the k−3/2⊥ spectra of the numerical MHD turbulence in the sense that they could be explained by assuming that fluctuations are polarised (aligned) approximately as inertial waves (Alfvén waves for MHD).

JFM classification

MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Rotating turbulence Turbulent Flows: Stratified turbulence

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Papers
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Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 134 - 153
Copyright
Copyright © Cambridge University Press 2011

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