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Direct numerical simulation of quasi-two-dimensional MHD turbulent shear flows

Published online by Cambridge University Press:  01 April 2021

Long Chen ,
Alban Pothérat Open the ORCID record for Alban Pothérat [Opens in a new window] ,
Ming-Jiu Ni Open the ORCID record for Ming-Jiu Ni [Opens in a new window]  and
René Moreau
Long Chen
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing101408, PR China
Alban Pothérat
Affiliation:
Fluid and Complex Systems Research Centre, Coventry University, CoventryCV15FB, UK
Ming-Jiu Ni*
Affiliation:
School of Engineering Science, University of Chinese Academy of Sciences, Beijing101408, PR China
René Moreau
Affiliation:
Laboratoire SIMAP, Groupe EPM, Université de Grenoble, BP 75, 38402Saint Martin d'Hères, France
*
†Email address for correspondence: [email protected]
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Abstract

High-resolution direct numerical simulations are performed to study the turbulent shear flow of liquid metal in a cylindrical container. The flow is driven by an azimuthal Lorentz force induced by the interaction between the radial electric currents injected through electrodes placed at the bottom wall and a magnetic field imposed in the axial direction. All physical parameters, are aligned with the experiment by Messadek & Moreau (J. Fluid Mech. vol. 456, 2002, pp. 137–159). The simulations recover the variations of angular momentum, velocity profiles, boundary layer thickness and turbulent spectra found experimentally to a very good precision. They further reveal a transition to small scale turbulence in the wall side layer when the Reynolds number based on Hartmann layer thickness $R$ exceeds 121, and a separation of this layer for $R \geq 145.2$. Ekman recirculations significantly influence these quantities and determine global dissipation. This phenomenology well captured by the 2-D PSM model (Pothérat, Sommeria & Moreau, J. Fluid Mech. vol. 424, 2000, pp. 75–100) until small-scale turbulence appears and incurs significant extra dissipation only captured by 3-D simulations. Secondly, we recover the theoretical law for the cutoff scale separating large quasi-two-dimensional (Q2-D) scales from small three-dimensional ones (Sommeria & Moreau, J. Fluid Mech. vol. 118, 1982, pp. 507–518), and thus establish its validity in sheared magnetohydrodynamics (MHD) turbulence. We further find that three-componentality and three-dimensionality appear concurrently and that both the frequency corresponding to the Q2-D cutoff scale and the mean energy associated with he axial component of velocity scale with the true interaction parameter $N_t$, respectively, as $0.063 N_t^{0.37}$ and $0.126N_t^{-0.92}$.

JFM classification

MHD and Electrohydrodynamics: MHD turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A130
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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