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Orthonormal Divergence-Free Wavelet Analysis of Energy Transfer in Hall MHD Turbulence

Keisuke ARAKI and Hideaki MIURA¹⁾

Okayama University of Science, 1-1 Ridai-cho, Okayama 700-0005, Japan

1)

National Institute for Fusion Science,322-6 Oroshi-cho, Toki 509-5292, Japan

(Received 9 December 2009 / Accepted 4 March 2010 / Published 10 December 2010)

Abstract

We studied the basic features of energy transfer in fully developed, freely decaying, isotropic, and homogeneous turbulence in magnetohydrodynamic (MHD) and Hall MHD (HMHD) media using orthonormal divergence-free wavelet analysis. The analysis supports the idea that energy transfer occurs locally; i.e., intense energy transfer occurs between modes that have very close spatial scales. The wavelet counterpart of triad interaction analysis in Fourier analysis shows that local interaction, i.e., combinations of three wavelet modes that have very close spatial scales, dominates the energy exchange between the velocity and magnetic fields. Energy transfer due to the Hall effect has opposite tendencies at larger and smaller scales, which is consistent with the results of Mininni et al. [P.D. Mininni et al., J. Plasma Phys. 73, 377 (2007)]. At larger scales, it causes a moderate inverse cascade. In contrast, it causes an intense forward cascade at smaller scales.

Copyright (c) 2010 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

Hall magnetohydrodynamics, fully developed turbulence, wavelet analysis, energy transfer

DOI: 10.1585/pfr.5.S2048

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This paper may be cited as follows:

Keisuke ARAKI and Hideaki MIURA, Plasma Fusion Res. 5, S2048 (2010).