Helical Mode Absolute Statistical Equilibrium of Ideal Three-Dimensional Hall Magnetohydrodynamics

Zhen-Wei Xia; Chun-Hua Li; Dan-Dan Zou; Wei-Hong Yang

doi:10.1088/0256-307X/34/1/015201

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Helical Mode Absolute Statistical Equilibrium of Ideal Three-Dimensional Hall Magnetohydrodynamics

¹Department of Modern Physics, University of Science and Technology of China, Hefei 230026
²Department of Information Engineering, Hefei University of Technology, Hefei 230009
³School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013

Funds: Supported by the National Natural Science Foundation of China under Grant Nos 11375190 and 11547137.

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Received Date: September 10, 2016

Published Date: December 31, 2016

Abstract

Abstract

Using the Fourier helical decomposition, we obtain the absolute statistical equilibrium spectra of left- and right-handed helical modes in the incompressible ideal Hall magnetohydrodynamics (MHD). It is shown that the left-handed helical modes play a major role on the spectral transfer properties of turbulence when the generalized helicity and magnetic helicity are both positive. In contrast, the right-handed helical modes will play a major role when both are negative. Furthermore, we also find that if the generalized helicity and magnetic helicity have opposite signs, the tendency of equilibrium spectra to condense at the large or small wave numbers will be presented in different helical sectors. This indicates that the generalized helicity dominates the forward cascade and the magnetic helicity dominates the inverse cascade properties of the Hall MHD turbulence.

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Helical Mode Absolute Statistical Equilibrium of Ideal Three-Dimensional Hall Magnetohydrodynamics

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