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On two-dimensional magnetohydrodynamic turbulence

Published online by Cambridge University Press:  19 April 2006

A. Pouquet
A. Pouquet
Affiliation:
Centre National de la Recherche Scientifique, Observatoire de Nice, France
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Abstract

It is shown that two-dimensional MHD turbulence is in certain respects closer to three-dimensional than to two-dimensional hydrodynamic turbulence. A second-order closure indicates that:

  1. at zero viscosity and magnetic diffusivity, a singularity appears at a finite time;

  2. there is an energy cascade to small scales and an inverse cascade of squared magnetic potential, in agreement with a conjecture of Fyfe & Montgomery (1976);

  3. small-scale magnetic energy acts like a negative eddy viscosity on large-scale magnetic fields;a

  4. (iv) upon injection of magnetic energy, a stationary state is obtained which has zero magnetic energy for a positive magnetic diffusivity λ (anti-dynamo theorem); however, this stationary state is preceded by a very long non-zero magnetic energy plateau which probably extends to infinite times as λ → 0.

It is suggested that direct numerical simulation of the two-dimensional MHD equations with high resolution (a 5122 or 10242 grid) could lead to a better understanding of the small-scale structure of fully developed turbulence, especially questions of intermittency and geometry.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 88 , Issue 1 , 13 September 1978 , pp. 1 - 16
Copyright
© 1978 Cambridge University Press

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