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Weak magnetohydrodynamic turbulence and intermittency

Published online by Cambridge University Press:  27 March 2015

R. Meyrand ,
K. H. Kiyani  and
S. Galtier
R. Meyrand
Affiliation:
Laboratoire de Physique des Plasmas, École Polytechnique, F-91128 Palaiseau CEDEX, France
K. H. Kiyani
Affiliation:
Laboratoire de Physique des Plasmas, École Polytechnique, F-91128 Palaiseau CEDEX, France Centre for Fusion, Space and Astrophysics, Department of Physics, University of Warwick, Coventry CV4 7AL, UK
S. Galtier*
Affiliation:
Laboratoire de Physique des Plasmas, École Polytechnique, F-91128 Palaiseau CEDEX, France
*
†Email address for correspondence: sebastien.galtier@lpp.polytechnique.fr
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Abstract

Three-dimensional numerical simulation is used to investigate intermittency in incompressible weak magnetohydrodynamic turbulence with a strong uniform magnetic field $\boldsymbol{b}_{\mathbf{0}}$ and zero cross-helicity. At leading order, this asymptotic regime is achieved via three-wave resonant interactions with the scattering of a wave on a 2D mode for which $k_{\Vert }=0$. When the interactions with the 2D modes are artificially reduced, we show numerically that the system exhibits an energy spectrum with $k_{\bot }^{-3/2}$, whereas the expected exact solution with $k_{\bot }^{-2}$ is recovered with the full nonlinear system. In the latter case, strong intermittency is found when the vector separation of structure functions is taken transverse to $\boldsymbol{b}_{\mathbf{0}}$. This result may be explained by the influence of the 2D modes whose regime belongs to strong turbulence. In addition to shedding light on the origin of this intermittency, we derive a log-Poisson law, ${\it\zeta}_{p}=p/8+1-(1/4)^{p/2}$, which fits the data perfectly and highlights the important role of parallel current sheets.

JFM classification

Turbulent Flows: Intermittency MHD and Electrohydrodynamics: MHD turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 770 , 10 May 2015 , R1
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Copyright
© 2015 Cambridge University Press 

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