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Dissipative, forced turbulence in two-dimensional magnetohydrodynamics

Published online by Cambridge University Press:  13 March 2009

David Fyfe ,
David Montgomery  and
Glenn Joyce
David Fyfe
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80303, U.S.A.
David Montgomery
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80303, U.S.A.
Glenn Joyce
Affiliation:
Department of Physics and Astronomy, The University of Iowa, Iowa City, Iowa 52242, U.S.A.
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Extract

The equations of motion for turbulent two-dimensional magnetohydrodynamic flows are solved in the presence of finite viscosity and resistivity, for the case in which external forces (mechanical and/or magnetic) act on the fluid. The goal is to verify the existence of a magnetohydrodynamic dynamo effect which is represented mathematically by a substantial back-transfer of mean square vector potential to the longest allowed Fourier wavelengths. External forces consisting of a random part plus a fraction of the value at the previous time step are employed, after the manner of Lilly for the Navier–Stokes case. The regime explored is that for which the mechanical and magnetic Reynolds numbers are in the region of 100 to 1000. The conclusions are that mechanical forcing terms alone cannot lead to dynamo action, but that dynamo action can result from either magnetic forcing terms or from both mechanical and magnetic forcing terms simultaneously. Most real physical cases seem most accurately modelled by the third situation. The spatial resolution of the 32 × 32 calculation is not adequate to test accurately the predictions of the spectral power laws previously arrived at on the basis of the assumption of simultaneous cascades of energy and vector potential. Some speculations are offered concerning possible relations between turbulent cascades and the ‘disruptive instability’.

Type
Research Article
Information
Journal of Plasma Physics , Volume 17 , Issue 3 , June 1977 , pp. 369 - 398
Copyright
Copyright © Cambridge University Press 1977

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