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Ion parallel viscosity and anisotropy in MHD turbulence

Published online by Cambridge University Press:  13 March 2009

Sean Oughton
Affiliation:
Department of Mathematics, University College London, Gower Street, London WCIE 6BT, UK

Abstract

We report on results from direct numerical simulation of the incompressible three- dimensional magnetohydrodynamic (MHD) equations, modified to incorporate viscous dissipation via the strongly anisotropic ion-parallel viscosity term. Both linear and nonlinear cases are considered, all with a strong background magnetic field. It is found that spectral anisotropy develops in almost all cases, but that the contribution from effects associated with the ion-parallel viscosity is relatively weak compared with the previously reported nonlinear process. Furthermore, and in contrast to this earlier work, it is suggested that when B0 is large, the anisotropy will develop and persist for many large-scale turnover times even for non-dissipative runs. Resistive dissipation is found to dominate over viscous even when the resistivity is several orders of magnitude smaller than the ion parallel viscosity. A variance anisotropy effect and anisotropy dependence on the polarization of the fluctuations are also observed.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

Batchelor, G. K. 1970 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bavassano, B., Dobrowolny, W., Fanfoni, G., Mariani, F. and Ness, N. F. 1982 Statistical properties of mhd fluctuations associated with high-speed streams from Helios-2 observations. Solar Phys. 78, 373.CrossRefGoogle Scholar
Belcher, J. W. and Davis, L. 1971 Large-amplitude Alfvén waves in the interplanetary medium, 2. J. Geophys. Res. 76, 3534.CrossRefGoogle Scholar
Bieber, J. W., Wanner, W. and Matthaeus, W. H. 1996 Dominant two-dimensional solar wind turbulence with implications for cosmic ray transport. J. Geophys. Res. 101, 2511.CrossRefGoogle Scholar
Book, D. L. 1987 NRL Plasma Formulary.NRL Publication 0084–4040, Washington, DC.Google Scholar
Braginskii, S. I. 1965 Transport processes in a plasma. Reviews of Plasma Physics (ed. Leontovich, M. A.), p. 205. Consultants Bureau, New York.Google Scholar
Carbone, V. and Veltri, P. 1990 A shell model for anisotropic magnetohydrodynamic turbulence. Geophys. & Astrophys. Fluid Dyn. 52, 153.CrossRefGoogle Scholar
Frisch, U., Pouquet, A.. Léorat, J. and Mazure, A. 1975 Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. J. Fluid Mech. 68, 769.CrossRefGoogle Scholar
Horbury, T., Balegh, A., Forsyth, R. J. and Smith, E. J. 1995 Anisotropy of inertial range turbulence in the polar heliosphere. Geophys. Rev. Lett. 22, 3405.CrossRefGoogle Scholar
Klein, L. W., Roberts, D. A. and Goldstein, M. L. 1991 Anisotropy and minimum variance directions of solar wind fluctuations in the outer heliosphere. J. Geophys. Res. 96, 3779.CrossRefGoogle Scholar
Kraichnan, R. H. 1965 Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8, 1385.Google Scholar
Kraichnan, R. H. and Montgomery, D.C. 1980 Two-dimensional turbulence. Rep. Prog. Phys. 43, 547.CrossRefGoogle Scholar
Lesieur, M. 1990 Turbulence in Fluids, 2nd ednKluwer, Dordrecht.Google Scholar
Matthaeus, W. H. and Goldstein, M. L. 1982 Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind. J. Geophys. Res. 87, 6011.Google Scholar
Matthaeus, W.H., Goldstein, M. L. and Roberts, D.A. 1990 Evidence for the presence of quasi-two-dimensional nearly incompressible fluctuations in the solar wind. J. Geophys. Res. 95, 20673.Google Scholar
Matthaeus, W.H., Ghosh, S., Oughton, S. and Roberts, D.A. 1996 Anisotropic three-dimensional mhd turbulence. J. Geophys. Res. 101, 7619.CrossRefGoogle Scholar
Moffatt, H. K. 1967 On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571.CrossRefGoogle Scholar
Montgomery, D. C. 1992 Modificaions of magnetohydrodynamics as applied to the solar wind. J. Geophys. Res. 97, 4309.CrossRefGoogle Scholar
Montgomery, D. C. and Matthaeus, W. H. 1995 Anisotropic modal energy transfer in interstellar turbulence. Astrophys. J. 447, 706.CrossRefGoogle Scholar
Montgomery, D.C. and Turner, L.. 1981 Anisotropic magnetohydrodynamic turbulence in a strong external magnetic field. Phys. Fluids 24, 825.CrossRefGoogle Scholar
Orszag, S. A. 1977 Lectures on the statistical theory of turbulence. Fluid Dynamics. Les Houches Summer School (ed. Balian, R. and Peube, J.-L.), 1973, p. 235. Gordon and Breach, New York.Google Scholar
Oughton, S. 1996 Energy dynamics in linear MHD with ion parallel viscosity. Submitted to J. Plasma Phys.Google Scholar
Oughton, S., Matthaeus, W. H. and Ghosh, S. 1995 Anisotropy in incompressible and compressible 3d mhd turbulence. Small-Scale Structures in Three-Dimensional Hydro and Magnetohydrodynamic Turbulence. Nice Workshop, January 1995 (ed. Meneguzzi, M., Pouquet, A. and Sulem, P. L.), p. 273. Lecture Notes in Physics, Vol. 462, Springer-Verlag, Berlin.CrossRefGoogle Scholar
Oughton, S., Priest, E. R. and Matthaeus, W. U. 1994 The influence of a mean magnetic field on three-dimensional MHD turbulence. J. Fluid Mech. 280, 95.CrossRefGoogle Scholar
Pouquet, A., Frisch, U. and Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77, 321.CrossRefGoogle Scholar
Robinson, D. and Rusbridge, M. 1971 Structure of turbulence in the zeta plasma. Phys. Fluids 14, 2499.Google Scholar
Shebalin, J. V., Matthaeus, W. H. and Montgomery, D. 1983 Anisotropy in MHD turbulence due to a mean magnetic field. J. Plasma Phys. 29, 525.CrossRefGoogle Scholar
Sridhar, S. and Goldreich, P. 1994 Toward a theory of interstellar turbulence: I. Weak Alfvénic turbulence. Astrophys. J. 432, 612.CrossRefGoogle Scholar
Stribling, T. and Matthaeus, V. H. 1990 Statistical properties of ideal three-dimensional magnetoliydrodynamics. Phys. Fluids B2, 1979.CrossRefGoogle Scholar
Stribling, T., Matthaeus, W.H. and Ghosh, S. 1994 Nonlinear decay of magnetic helicity in magnetohydrodynamics with a mean magnetic field. J. Geophys. Res. 99, 2567.Google Scholar
Stribling, T., Matthaeus, W. H. and Oughton, S. 1995 Magnetic helicity in magnetoliydrodynamic turbulence with a mean magnetic field. Phys. Plasmas 2, 1437.Google Scholar
Zhou, V. and Matthaeus, W. H. 1990 Transport and turbulence modeling of solar wind fluctuations. J. Geophys. Res. 95, 10291.CrossRefGoogle Scholar
Zweben, S., Menyuk, C. and Taylor, R. 1979 Small-scale magnetic fluctuations inside the macrotor tokamak. Phys.Rev. Lett. 42, 1270.CrossRefGoogle Scholar