Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T04:43:37.023Z Has data issue: false hasContentIssue false
  • English
  • Français

Stationary states of two-dimensional magnetohydrodynamic turbulence: non-dissipative limit

Published online by Cambridge University Press:  13 March 2009

Ronald Calinon  and
Danilo Merlini
Ronald Calinon
Affiliation:
Département do Physique, Ecole Polytechnique Fédérale de Lausanne, CH-1007 Lausanne, Switzerland
Danilo Merlini
Affiliation:
Department of Physics, College of William and Mary, Williamsburg, Virginia 23185
Get access Rights & Permissions [Opens in a new window]

Abstract

A class of exact stationary statistical states for the inviscid magnetohydrodynamic equations in two dimensions and in various geometries is found and the corresponding fluctuation spectra are calculated. Some solutions agree with previous computations in the canonical ensemble while other solutions are found. In particular, the Navier—Stokes limit is recovered and maximum cross helicity solutions exist in two dimensions. The difficulty of proving existence and uniqueness of statistical solutions for non-dissipative two-dimensional turbulence is quoted in terms of rugged constants and associated Gibbs measure.

Type
Research Article
Information
Journal of Plasma Physics , Volume 22 , Issue 3 , December 1979 , pp. 385 - 396
Copyright
Copyright © Cambridge University Press 1979

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

Calinon, R. & Merlini, D. 1978 Preprint.Google Scholar
Cook, I. & Taylor, J. B. 1971 Phys. Rev. Lett. 28, 82.CrossRefGoogle Scholar
Dupree, T. H. 1974 Phys. Fluids, 17, 100.CrossRefGoogle Scholar
Edwards, J. 1973 Proceedings of the Cuiham Conference on Strong Turbulence.Google Scholar
Fyfe, D., Joyce, G. & Montgomery, D. 1977 a J. Plasma Phys. 17, 317.CrossRefGoogle Scholar
Fyfe, D & Montgomery, D. 1976 J. Plasma Phys. 16, 181.CrossRefGoogle Scholar
Fyfe, D. & Montgomery, D. 1978 Phys. Fluids, 21, 316.CrossRefGoogle Scholar
Fyfe, D., Montgomery, D. & Joyce, D. 1977 b J. Plasma Phys. 17, 369.CrossRefGoogle Scholar
Gallavotti, G. 1976 a Problémes ergodiques de la mécanique classique, Cour 30% cycle, EPFL Lausanne.Google Scholar
Gallavotti, G. 1976 b Annali di Mat. Serie IV, 108, 227.CrossRefGoogle Scholar
Hopf, E. 1952 J. Rat. Mech. Analysis, 1, 87.Google Scholar
Knorr, G. 1977 J. Plasma Phys. 19, 121.Google Scholar
Kraichnan, R. H. 1965 Phys. Fluids, 8, 1385.CrossRefGoogle Scholar
Kraicknan, R. H. 1967 Phys. Fluids, 10, 1417.CrossRefGoogle Scholar
Marchioro, C., Pellegrinotti, A. & Presutti, B. 1975 Comm. Math. Phys. 40, 175.CrossRefGoogle Scholar
Mond, M. & Knorr, G. 1978 J. Plasma Phys. 19, 121.CrossRefGoogle Scholar
Merlini, D. et al. 1979 (in preparation).Google Scholar
Montgomery, D. 1977 Eastern Physics Congress, Williamsburg, VA.Google Scholar
Montgomery, D. & Vahala, G. 1979 J. Plasma Phys. 21, 71.CrossRefGoogle Scholar