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Do magnetic fields enhance turbulence at low magnetic Reynolds number?

Alban Pothérat1,2,* and Rico Klein1

  • 1Applied Mathematics Research Centre, Coventry University, Priory Street, Coventry CV1 5FB, United Kingdom
  • 2Laboratoire National des Champs Magnétiques Intenses, Université Grenoble Alpes, CNRS, 25 Rue des Martyrs, Boîte Postale 166, 38042 Grenoble Cedex, France

  • *alban.potherat@coventry.ac.uk
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Phys. Rev. Fluids 2, 063702 – Published 30 June, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.063702

Abstract

Imposing a magnetic field on a turbulent flow of electrically conducting fluid incurs the Joule effect. A current paradigm is that the corresponding dissipation increases with the intensity of the magnetic field and as a result turbulent fluctuations are all the more damped as the magnetic field is strong. While this idea finds apparent support in the phenomenology of decaying turbulence, measurements of turbulence in duct flows and other, more complex configurations have produced seemingly contradicting results. The root of the controversy is that magnetic fields promote sufficient scale-dependent anisotropy to profoundly reorganize the structure of turbulence, so their net effect cannot be understood in terms of the additional dissipation only. Here we show that when turbulence is forced in a magnetic field that acts on turbulence itself rather than on the mechanisms that generate it, the field promotes large, nearly two-dimensional structures capturing sufficient energy to offset the loss due to Joule dissipation, with the net effect of increasing the intensity of turbulent fluctuations. This change of paradigm potentially carries important consequences for systems as diverse as the liquid cores of planets, accretion disks, and a wide range of metallurgical and nuclear engineering applications.

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Phys. Rev. Fluids 2, 063702– Published 30 June, 2017
  • Received 26 July 2016

©2017 American Physical Society

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