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On the decay of low-magnetic-Reynolds-number turbulence in an imposed magnetic field

Published online by Cambridge University Press:  26 March 2010

N. OKAMOTO ,
P. A. DAVIDSON  and
Y. KANEDA
N. OKAMOTO
Affiliation:
Center for Computational Science, Nagoya University, Nagoya 464-8603, Japan
P. A. DAVIDSON*
Affiliation:
Department of Engineering, University of Cambridge, Trumpington Street, Cambridge CB2 1PZ, UK
Y. KANEDA
Affiliation:
Department of Computational Science and Engineering, Nagoya University, Nagoya 464-8603, Japan
*
†Email address for correspondence: pad3@eng.cam.ac.uk
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Abstract

We examine the integral properties of freely decaying homogeneous magnetohydrodynamic (MHD) turbulence subject to an imposed magnetic field B0 at low-magnetic Reynolds number. We confirm that, like conventional isotropic turbulence, the fully developed state possesses a Loitsyansky-like integral invariant, in this case I// = − ∫ r⊥2 〈 u⊥·u′⊥〉 dr, where 〈u(x) ·u(x + rc)〉 = 〈u·u′〉 is the usual two-point velocity correlation and the subscript ⊥ indicates components perpendicular to the imposed field. The conservation of I// for fully developed turbulence places a fundamental restriction on the way in which the integral scales can develop, i.e. it implies u⊥2 ℓ⊥4 ℓ// ≈ constant where u⊥, ℓ⊥ and ℓ// are integral scales. This constraint can be used to estimate the evolution of u⊥(t; B0), ℓ⊥(t; B0) and ℓ//(t; B0), and these theoretical decay laws are shown to be in good agreement with numerical simulations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 651 , 25 May 2010 , pp. 295 - 318
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Batchelor, G. K. & Proudman, I. 1956 The large-scale structure of homogeneous turbulence. Phil. Trans. R. Soc. Lond. A 248, 369–405.Google Scholar
Bigot, B., Galtier, S. & Politano, H. 2008 Energy decay laws in strongly anisotropic magnetohydrodynamic turbulence. Phys. Rev. Lett. 100, 074502.CrossRefGoogle ScholarPubMed
Davidson, P. A. 1995 Magnetic damping of jets and vortices. J. Fluid Mech. 299, 153–186.CrossRefGoogle Scholar
Davidson, P. A. 1997 The role of angular momentum in the magnetic damping of turbulence. J. Fluid Mech. 336, 123–150.CrossRefGoogle Scholar
Davidson, P. A. 1999 Magnetohydrodynamics in material processing. Annu. Rev. Fluid Mech. 31, 273–300.CrossRefGoogle Scholar
Davidson, P. A. 2001 An Introduction to Magnetohydrodynamics. Cambridge University Press.CrossRefGoogle Scholar
Davidson, P. A. 2004 Turbulence: An Introduction for Scientists and Engineers. Oxford University Press.Google Scholar
Davidson, P. A. 2009 The role of angular momentum conservation in homogeneous turbulence. J. Fluid Mech. 632, 329–358.CrossRefGoogle Scholar
Ishida, T., Davidson, P. A. & Kaneda, Y. 2006 On the decay of isotropic turbulence. J. Fluid Mech. 564, 455–475.CrossRefGoogle Scholar
Kolmogorov, A. N. 1941 On the degeneration of isotropic turbulence in an incompressible viscous fluid. Dokl. Akad. Nauk. SSSR 31 (6), 538–541.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1959 Fluid Mechanics, 1st edn.Pergamon.Google Scholar
Moffatt, H. K. 1967 On the suppression of turbulence by a uniform magnetic field. J. Fluid Mech. 28, 571–592.CrossRefGoogle Scholar
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.Google Scholar
Roberts, P. H. 1967 An Introduction to Magnetohydrodynamics. Elsevier.Google Scholar