[Table of Contents]

Plasma and Fusion Research

Volume 5, S2048 (2010)

Regular Articles

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
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)


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.


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

DOI: 10.1585/pfr.5.S2048


  • [1] K. Itoh et al., Phys. Plasmas 12, 062303 (2005).
  • [2] S. M. Mahajan and Z. Yoshida, Phys. Plasmas 7, 635 (2000).
  • [3] S. Balbus and C. Terquem, Astrophys. J. 552, 235 (2001).
  • [4] J. Shiraishi, S. Ohsaki and Z. Yoshida, Phys. Plasmas 12, 092901 (2005).
  • [5] P. D. Mininni, A. Alexakis and A. Pouquet, J. Plasma Phys. 73, 377 (2007).
  • [6] K. Kishida, K. Araki, K. Suzuki and S. Kishiba, PRL 83, 5487 (1999).
  • [7] K. Araki and H. Miura, “Orthonormal Divergence-free Wavelet Analysis of Nonlinear Energy Transfer in RollingUp Vortices”, Y. Kaneda (ed.), IUTAM symposium on Computational Physics and New Perspectives in Turbulence, 149 (2008).
  • [8] K. Araki and H. Miura, J. Plasma Fusion Res. SERIES 9, 446 (2010).
  • [9] H. Miura and D. Hori, J. Plasma Fusion Res. SERIES 8, 73 (2009).
  • [10] A. Alexakis, P. D. Mininni and A. Pouquet, Phys. Rev. E 72, 046301 (2005).
  • [11] K. Araki and H. Miura, J. Plasma Fusion Res. SERIES 8, 96 (2009).

This paper may be cited as follows:

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