Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-29T17:13:33.877Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Brachet, M. E., Meiron, D. I., Orszag, S. A., Nickel, B. G., Morf, R. H. & Frisch, U. 1983 J. Fluid Mech. 130, 411.CrossRefGoogle Scholar
Bullough, R. K., Caudrey, P. J. & Gibbs, H. M. 1980 Solitons (ed. R. K. Bullough and P. J. Caudrey), p. 107.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Magnetohydrodynamic Stability. Oxford University Press.Google Scholar
Chapman, S. & Kendall, P. C. 1963 Proc. Roy. Soc. A 271, 435.Google Scholar
Dodd, R. K. & Bullough, R. K. 1976 Proc. Roy. Soc. A 351, 499.Google Scholar
Dungey, J. W. 1953 Phil. Mag. 44, 725.CrossRefGoogle Scholar
Forbes, T. G. & Speiser, T. W. 1979 J. Plasma Phys. 21, 107.CrossRefGoogle Scholar
Frisch, U. 1983 Chaotic Behaviour of Deterministic Systems, Les Hauches Summer School 1981, p. 666. North Holland.Google Scholar
Frisch, U., Pouquet, A., Sulem, P. L. & Meneguzzi, M. 1983 J. Méc. Théor. Appl.; Special issue on Two-dimensional turbulence, p. 191.Google Scholar
Glassey, R. 1981 Math. Z. 177, 323.CrossRefGoogle Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. SIAM.CrossRefGoogle Scholar
Imshennik, S. & Syrovatskii, S. I. 1967 Soviet Phys. JETP, 25, 656.Google Scholar
Kato, T. 1980 Comm. Pure Appl. Math. 33, 501.CrossRefGoogle Scholar
Matthaeus, W. H. & Montgomery, D. 1981 J. Plasma Phys. 25, 11.CrossRefGoogle Scholar
Morf, R. H., Orszag, S. A., Meiron, D. I., Frisch, U. & Meneguzzi, M. 1981 Lecture Notes in Physics, vol. 141, p. 282. Springer.Google Scholar
Orszag, S. A. & Patterson, G. S. 1972. Phys. Rev. Lett. 28, 76.CrossRefGoogle Scholar
Orszag, S. A. & Tang, C. M. 1979 J. Fluid Mech. 90, 129.CrossRefGoogle Scholar
Pouquet, A. 1978 J. Fluid Mech. 88, 1.CrossRefGoogle Scholar
Sulem, C., Sulem, P. L. & Frisch, H. 1983 J. Comp. Phys. 50, 138.CrossRefGoogle Scholar
Syrovatskii, S. I. 1981 Ann. Rev. Astron. Astrophys. 19, 163.CrossRefGoogle Scholar
Uberoi, M. S. 1963 Phys. Fluids, 6, 1379.CrossRefGoogle Scholar