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

Long Chen, Alban Potherat, Mingjiu Ni, Rene Moreau

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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 exceeds 121, and a separation of this layer for. 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, respectively, as and.

Original languageEnglish
Article number2100103
Number of pages35
JournalJournal of Fluid Mechanics
Early online date1 Apr 2021
Publication statusPublished - 25 May 2021

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NSFC under grant nos. 51636009, 51606183 and CAS under grant nos. XDB22040201, QYZDJ-SSW-SLH014.


  • MHD turbulence
  • magnetohydrodynamics

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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