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Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence

Published online by Cambridge University Press:  07 March 2007

T. A. YOUSEF ,
F. RINCON  and
A. A. SCHEKOCHIHIN
T. A. YOUSEF
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
F. RINCON
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
A. A. SCHEKOCHIHIN
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
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Abstract

This paper examines the consistency of the exact scaling laws for isotropic magnetohydrodynamic (MHD) turbulence in numerical simulations with large magnetic Prandtl numbers Pm and with Pm = 1. The exact laws are used to elucidate the structure of the magnetic and velocity fields. Despite the linear scaling of certain third-order correlation functions, the situation is not analogous to the case of Kolmogorov turbulence. The magnetic field is adequately described by a model of a stripy (folded) field with direction reversals at the resistive scale. At currently available resolutions, the cascade of kinetic energy is short-circuited by the direct exchange of energy between the forcing-scale motions and the stripy magnetic fields. This non-local interaction is the defining feature of isotropic MHD turbulence.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 575 , March 2007 , pp. 111 - 120
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Alexakis, A., Mininni, P. D. & Pouquet, A. 2005 Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence. Phys. Rev. E 72, 0463 01.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1950 On the spontaneous magnetic field in a conducting liquid in turbulent motion. Proc. R. Soc. Lond. A 201, 405–416.Google Scholar
Berti, S., Bistagnino, A., Boffetta, G., Celani, A. & Musacchio, S. 2006 Small scale statistics of viscoelatic turbulence. Europhys. Lett., submitted (e-print nlin.CD/0606043).CrossRefGoogle Scholar
Biskamp, D. & Müller, W.-C. 2000 Scaling properties of isotropic three-dimensional magnetohydrodynamic turbulence. Phys. Plasmas 7, 4889–4900.CrossRefGoogle Scholar
Brandenburg, A. 2001 The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence. Astrophys. J. 550, 824–840.CrossRefGoogle Scholar
Chandrasekhar, S. 1951 The invariant theory of isotropic turbulence in magneto-hydrodynamics. Proc. R. Soc. Lond. A 204, 435–449.Google Scholar
DeAngelis, E. Angelis, E., Cassciola, C. M., Benzi, R. & Piva, R. 2005 Homogeneous isotropic turbulence in dilute polymers. J. Fluid Mech. 531, 1–10.Google Scholar
Haugen, N. E. L., Brandenburg, A. & Dobler, W. 2004 Simulations of nonhelical hydromagnetic turbulence. Phys. Rev. E 70, 016308.CrossRefGoogle ScholarPubMed
Kazantsev, A. P. 1968 Enhancement of a magnetic field by a conducting fluid. Sov. Phys. JETP 26, 1031–1034.Google Scholar
Moffatt, H. K. 1963 Magnetic eddies in an incompressible viscous fluid of high electrical conductivity. J. Fluid Mech. 17, 225–239.CrossRefGoogle Scholar
Moffatt, H. K. & Saffman, P. G. 1964 Comment on “Growth of a weak magnetic field in a turbulent conducting fluid with large magnetic Prandtl number”. Phys. Fluids 7, 155.CrossRefGoogle Scholar
Politano, H. & Pouquet, A. 1998 a Dynamical length scales for turbulent magnetized flows. Geophys. Res. Lett. 25, 273–27.CrossRefGoogle Scholar
Politano, H. & Pouquet, A. 1998 b v on Kármán-Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys. Rev. E 57, R21–R24.CrossRefGoogle Scholar
Rincon, F. 2006 Anisotropy, inhomogeneity and inertial range scalings in turbulent convection. J. Fluid Mech. 563, 43–69.CrossRefGoogle Scholar
Schekochihin, A. A. & Cowley, S. C. 2006 Turbulence and magnetic fields in astrophysical plasmas. In Magnetohydrodynamics: Historical Evolution and Trends (ed. Molokov, S., Moreau, R. & Moffatt, H. K.). Berlin: Springer, in press (e-print astro-ph/0507686).Google Scholar
Schekochihin, A. A., Cowley, S. C., Hammett, G. W., Maron, J. L. & McWilliams, J. C. 2002 A model of nonlinear evolution and saturation of the turbulent MHD dynamo. New J. Phys. 4, 84.CrossRefGoogle Scholar
Schekochihin, A. A., Cowley, S. C., Taylor, S. F., Maron, J. L. & McWilliams, J. C. 2004 Simulations of the small-scale turbulent dynamo. Astrophys. J. 612, 276–307.CrossRefGoogle Scholar
Schlüter, A. & Biermann, L. 1950 Interstellare magnetfelder. Z. Naturforsch. 5a, 237–351.CrossRefGoogle Scholar