Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-29T13:25:46.788Z Has data issue: false hasContentIssue false

Inverse cascades in incompressible fluid and magnetofluid turbulence

Published online by Cambridge University Press:  13 March 2009

Murshed Hossain
Affiliation:
Bartol Research Institute, University of Delaware, Newark, DE 19716, USA

Abstract

Absolute equilibrium statistical theory and numerical simulations are reviewed in the context of inverse cascades in two- and three-dimensional incompressible fluid and magnetofluid turbulence. Turbulent fluctuations of physically interesting quantities undergo inverse cascade to larger spatial scales, leading to self-organization under certain circumstances. In particular, most systems with more than one quadratic ideal invariant, or, having some kind of imposed anisotropy, exhibit inverse cascades. Anisotropic fluid turbulence in the presence of a uniform rotation and magnetofluid turbulence in the presence of a uniform magnetic field are considered.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

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

Alemany, A., Moreau, R., Sulem, P. L. and Frisch, U. 1979 J. Méc. 18, 277.Google Scholar
Birch, P. 1982 Nature 298, 451.CrossRefGoogle Scholar
Branover, H., Sukoriansky, S., Talmage, G. and Greenspan, E. 1986 Fusion Technol. 10, 822.CrossRefGoogle Scholar
Fjortoft, R. 1953 Tellus 5, 225.CrossRefGoogle Scholar
Frisch, U., Pouquet, A., Leorat, J. and Mazure, A. 1975 J. Fluid Mech. 68, 769.CrossRefGoogle Scholar
Fyfe, D. and Montgomery, D. 1976 J. Plasma Phys. 16, 181.CrossRefGoogle Scholar
Fyfe, D., Joyce, G.. and Montgomery, D. 1977 a J. Plasma Phys. 17, 317.CrossRefGoogle Scholar
Fyfe, D., Montgomery, D. and Joyce, G. 1977 b J. Plasma Phys. 17, 369.CrossRefGoogle Scholar
Ghosh, S., Matthaeus, W. H. and Montgomery, D. 1988 Phys. Fluids 31, 2171.CrossRefGoogle Scholar
Grant, H. L., Stewart, R. W. and Moilliet, A. 1962 J. Fluid Mech. 12, 241.CrossRefGoogle Scholar
Hasegawa, A. 1985 Adv. Phys. 34, 1.CrossRefGoogle Scholar
Hossain, M. 1983 PhD dissertation, College of William and Mary.Google Scholar
Hossain, M. 1991 Phys. Fluids B3, 511.CrossRefGoogle Scholar
Hossain, M. 1994 a Phys. Fluids 6, 1077.CrossRefGoogle Scholar
Hossain, M. 1994 b Current Topics in the Physics of Fluids (ed. Alexander, J. C. and Menon, J.), Vol. 1, p. 207. Research Trends, Trivandrum, India.Google Scholar
Hossain, M., Matthaeus, W. H. and Montgomery, D. 1983 J. Plasma Phys. 30, 479.CrossRefGoogle Scholar
Hossain, M., Vahala, G.. and Montgomery, D. 1985 Phys. Fluids 28, 3074.CrossRefGoogle Scholar
Hossain, M., Gray, P. C., Pontius, D. H., Matthaeus, W. H. and Oughton, S. 1995 Phys. Fluids 7, 2886.CrossRefGoogle Scholar
Kármán, T. von and Howarth, L. 1938 Proc. R. Soc. Lond. A164, 192.Google Scholar
Kolmogorov, A. N. 1941 Dokl. Akad. Nauk SSSR 30, 301.Google Scholar
Kraichnan, R. H. 1967 Phys. Fluids 10, 1417.CrossRefGoogle Scholar
Kraichnan, R. H. 1973 J. Fluid Mech. 59, 745.CrossRefGoogle Scholar
Kraichnan, R. H. 1975 J. Fluid Mech. 67, 155.CrossRefGoogle Scholar
Kraichnan, R. H. and Montgomery, D. 1980 Rep. Prog. Phys. 43, 547.CrossRefGoogle Scholar
Krishan, V. 1991 Solar Interior and Atmosphere (ed. Cox, A. N., Livingston, W. C. and Matthews, M. S.), pp. 10291043. University of Arizona Press, Tucson.Google Scholar
Krishan, V. and Sivaram, C. 1991 Mon. Not. R. Astron. Soc. 250, 157.CrossRefGoogle Scholar
Lee, T. D. 1952 Q. Appl. Maths 10, 69.CrossRefGoogle Scholar
Leith, C. E. 1968 Phys. Fluids 11, 671.CrossRefGoogle Scholar
Lilly, D. K. 1969 Phys. Fluids 12 (Suppl. II), 240.CrossRefGoogle Scholar
McWilliams, J. C. 1984 J. Fluid Mech. 146, 21.CrossRefGoogle Scholar
Marcus, P. S. 1993 Ann. Rev. Astron. Astrophys. 31, 523.CrossRefGoogle Scholar
Matthaeus, W. H., Stribling, W. T., Martinez, D., Oughton, S. and Montgomery, D. 1991 a Phys. Rev. Lett. 66, 2731.CrossRefGoogle Scholar
Matthaeus, W. H., Stribling, W. T., Martinez, D., Oughton, S. and Montgomery, D. 1991 b Physica D51, 531.Google Scholar
Meneguzzi, M., Frisch, U. and Pouquet, A. 1981 Phys. Rev. Lett. 47, 1060.CrossRefGoogle Scholar
Moffatt, H. K. 1967 J. Fluid Mech. 28, 571.CrossRefGoogle Scholar
Montgomery, D 1982 Physica Scripta T2/1, 83.CrossRefGoogle Scholar
Nakauchi, N., Oshima, H. and Saito, Y. 1992 Phys. Fluids A4, 2906.CrossRefGoogle Scholar
Oughton, S., Priest, E. R. and Matthaeus, W. H.. 1994 J. Fluid Mech. 280, 95.CrossRefGoogle Scholar
Proudman, J. 1916 Proc. R. Soc. Lond. A92, 408.Google Scholar
Roberts, P. H. 1967 An Introduction to Magnetohydrodynamics. Elsevier, New York.Google Scholar
Seyler, C. E., Salu, Y., Montgomery, D. and Knorr, G. 1975 Phys. Fluids 18, 803.CrossRefGoogle Scholar
Shebalin, J. V., Matthaeus, W. H. and Montgomery, D. 1983 J. Plasma Phys. 29, 525.CrossRefGoogle Scholar
Smith, L. M. and Yakhot, V. 1993 Phys. Rev. Lett. 71, 352.CrossRefGoogle Scholar
Sommeria, J. 1986 J. Fluid Mech. 170, 139.CrossRefGoogle Scholar
Sommeria, J. and Moreau, R. 1982 J Fluid Mech. 118, 507.CrossRefGoogle Scholar
Strauss, H. R. 1976 Phys. Fluids 19, 134.CrossRefGoogle Scholar
Stribling, T. and Matthaeus, W. H. 1990 Phys. Fluids B2, 1979.CrossRefGoogle Scholar
Sukoriansky, S. and Branover, H. 1988 Current Trends in Turbulence Research (ed. Branover, H., Mond, M. and Unger, Y.). AIAA, Washington, DC.Google Scholar
Taylor, G. I. 1921 Proc. R. Soc. Lond. A104, 213.Google Scholar
Tritton, D. J. 1988 Physical Fluid Dynamics, 2nd edn. Oxford University Press.Google Scholar