Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-15T01:43:53.305Z Has data issue: false hasContentIssue false
  • English
  • Français

Long-time states of inverse cascades in the presence of a maximum length scale

Published online by Cambridge University Press:  13 March 2009

Murshed Hossain ,
William H. Matthaeus  and
David Montgomery
Murshed Hossain
Affiliation:
Physics Department, College of William and Mary, Williamsburg, Virginia 23185, U.S.A.
William H. Matthaeus
Affiliation:
Physics Department, College of William and Mary, Williamsburg, Virginia 23185, U.S.A.
David Montgomery
Affiliation:
Physics Department, College of William and Mary, Williamsburg, Virginia 23185, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

It is shown numerically, both for the two-dimensional Navier-Stokes (guidingcentre plasma) equations and for two-dimensional magnetohydrodynamics, that the long-time asymptotic state in a forced inverse-cascade situation is one in which the spectrum is completely dominated by its own fundamental. The growth continues until the fundamental is dissipatively limited by its own dissipation rate.

Type
Research Article
Information
Journal of Plasma Physics , Volume 30 , Issue 3 , December 1983 , pp. 479 - 493
Copyright
Copyright © Cambridge University Press 1983

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

Batchelor, G. K. 1969 Phys. Fluids, 12, Suppl. II, 233.CrossRefGoogle Scholar
Burg, J. P. 1975 Ph.D. dissertation, Stanford University.Google Scholar
Carnevale, G. F., Frisch, U. & Salmon, R. 1981 J. Phys. A, 14, 1701.CrossRefGoogle Scholar
Fjørtoft, R. 1953 Tellus, 5, 225.CrossRefGoogle Scholar
Frisch, U., Pouquet, A., Léorat, J. & Mazure, A. 1975 J. Fluid Mech. 68, 769.CrossRefGoogle Scholar
Frisch, U., Pouquet, A., Sulem, P.-L. & Meneguzzi, M. 1983 J. de Mécanique Théorique et Appliquée. (To be published).Google Scholar
Fyfe, D., Joyce, G. & Montgomery, D. 1977 a J. Plasma Phys. 17, 317.CrossRefGoogle Scholar
Fyfe, D., Joyce, G. & Montgomery, D. 1977 b J. Plasma Phys. 17, 369.CrossRefGoogle Scholar
Fyfe, D. & Montgomery, D. 1976 J. Plasma Phys. 16, 181.CrossRefGoogle Scholar
Gottlieb, D. & Orszag, S. A. 1977 Numerical Analysis of Spectral Methods: Theory and Applications. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar
Kraichnan, R. H. 1967 Phys. Fluids, 10, 1417.CrossRefGoogle Scholar
Kraichnan, R. H. & Montgomery, D. 1980 Rep. Prog. Phys. 43, 547.CrossRefGoogle Scholar
Leith, C. E. 1968 Phys. Fluids, 11, 671.CrossRefGoogle Scholar
Lilly, D. K. 1969 Phys. Fluids, 12, Suppl. II, 240.CrossRefGoogle Scholar
Matthaeus, W. H. 1982 Geophys. Res. Lett. 9, 660.CrossRefGoogle Scholar
Matthaeus, W. H. & Montgomery, D. 1980 Ann. N.Y. Acad. Sci. 357, 203.CrossRefGoogle Scholar
Matthaeus, W. H. & Montgomery, D. 1981 J. Plasma Phys. 25, 11.CrossRefGoogle Scholar
Meneguzzi, M., Frisch, U. & Pouquet, A. 1981 Phys. Rev. Lett. 47, 1060.CrossRefGoogle Scholar
Montgomery, D. 1975 Plasma Physics Les Houches 1972 (ed. de Witt, C. and Peyraud, J.), p. 427. Gordon & Breach.Google Scholar
Onsager, L. 1949 Nuovo Cimento Suppl. 6, 279.CrossRefGoogle Scholar
Orszag, S. A. 1971 Stud. Appl. Math. 50, 293.CrossRefGoogle Scholar
Orszag, S. A. & Tang, C.-M. 1979 J. Fluid Mech. 90, 129.CrossRefGoogle Scholar
Patterson, G. S. & Orszag, S. A. 1971 Phys. Fluids, 14, 2538.CrossRefGoogle Scholar
Pouquet, A. 1978 J. Fluid Mech. 88, 1.CrossRefGoogle Scholar
Pouquet, A., Frisch, U. & Léorat, J. 1976 J. Fluid Mech. 77, 321.CrossRefGoogle Scholar