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Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence

Published online by Cambridge University Press:  31 July 2019

Riddhi Bandyopadhyay Open the ORCID record for Riddhi Bandyopadhyay [Opens in a new window] ,
William H. Matthaeus Open the ORCID record for William H. Matthaeus [Opens in a new window] ,
Sean Oughton Open the ORCID record for Sean Oughton [Opens in a new window]  and
Minping Wan Open the ORCID record for Minping Wan [Opens in a new window]
Riddhi Bandyopadhyay
Affiliation:
Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA Bartol Research Institute, University of Delaware, Newark, DE 19716, USA
William H. Matthaeus*
Affiliation:
Department of Physics and Astronomy, University of Delaware, Newark, DE 19716, USA Bartol Research Institute, University of Delaware, Newark, DE 19716, USA
Sean Oughton
Affiliation:
Department of Mathematics and Statistics, University of Waikato, Hamilton 3240, NZ
Minping Wan
Affiliation:
Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China
*
†Email address for correspondence: [email protected]
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Abstract

In an earlier paper (Wan et al., J. Fluid Mech., vol. 697, 2012, pp. 296–315), the authors showed that a similarity solution for anisotropic incompressible three-dimensional magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\boldsymbol{B}_{0}$, exists if the ratio of parallel to perpendicular (with respect to $\boldsymbol{B}_{0}$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor–Kármán-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, mean field strength, and cross-helicity, on the nature of similarity decay is discussed.

JFM classification

Turbulent Flows: Homogeneous turbulence MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 5 - 18
Copyright
© 2019 Cambridge University Press 

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