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On the exponential flattening of current sheets near neutral X-points in two-dimensional ideal MHD flow

Published online by Cambridge University Press:  13 March 2009

P. L. Sulem ,
U. Frisch ,
A. Pouquet  and
M. Meneguzzi
P. L. Sulem
Affiliation:
CNRS, Observatoire de Nice, 06-Nice, France
U. Frisch
Affiliation:
CNRS, Observatoire de Nice, 06-Nice, France
A. Pouquet
Affiliation:
CNRS, Observatoire de Nice, 06-Nice, France
M. Meneguzzi
Affiliation:
Service d'Astrophysique, GEN Saclay and CNRS, France
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Abstract

It is shown that the flattening of current sheets which has been observed near neutral X-points in numerical simulations of ideal MHD flow in two dimensions can be obtained from an asymptotic expansion of the dynamical equations. This asymptotic expansion suggests that exponential self-similar flattening proceeds forever and that there is no finite time singularity for ideal two-dimensional MHD flows. The equation for the spatial structure of the self-similar solution is reduced, via a hodograph transformation, to a nonlinear wave equation involving interactions with distant parts of the fluid and therefore non-universal features.

Type
Research Article
Information
Journal of Plasma Physics , Volume 33 , Issue 2 , April 1985 , pp. 191 - 198
Copyright
Copyright © Cambridge University Press 1985

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