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Conference on Turbulence and Interactions TI2006 May June Porquerolles France

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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France Anisotropy of transport properties in magnetohydrodynamic turbulent flows Maxime Kinet†,?, Bernard Knaepen†, Daniele Carati† † Universite Libre de Bruxelles, Physique Statistique et des Plasmas, Campus Plaine CP231, B-1050 Bruxelles, Belgium ?Email: ABSTRACT Direct numerical simulations of a passive scalar in a turbulent conducting flow subject to an externally applied magnetic field are performed. The magnetohydrodynamics (MHD for short) equations are solved numerically, in parallel with an advection-diffusion equation for the passive scalar, using a spectral resolution of 2563 Fourier modes. The Magnetic Reynolds number is assumed to be lower than unity, so that the quasi- static approximation can be used. Turbulence statistics are computed to study the anisotropy induced by the magnetic field in the flow as well as in the scalar distribution. INTRODUCTION Conducting fluids are encountered in many in- dustrial and technological applications, from the fabrication of semi-conductors crystals to the de- sign of efficient cooling blankets for future fusion reactors (tokamaks). For most laboratory flows, the magnetic Reynolds number Rm = UL/? is very low (here ? is the magnetic diffusivity while U and L represent characteristic velocity and length scales for the flow considered). In that case, an applied magnetic field can strongly affect the fluid's motion but there is practically no retroaction of the flow on the applied field.

  • angular spec- tra

  • field

  • fonds na- tional pour la recherche scientifique

  • turbulent conducting

  • passive scalar

  • scalar energy

  • magnetic field


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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France
Anisotropy of transport properties in magnetohydrodynamic turbulent flows
,∗ † Maxime Kinet, Bernard Knaepen, Daniele Carati Universit´eLibredeBruxelles,PhysiqueStatistiqueetdesPlasmas, Campus Plaine CP231, B-1050 Bruxelles, Belgium Email: mkinet@ulb.ac.be
ABSTRACT Direct numerical simulations of a passive scalar in a turbulent conducting flow subject to an externally applied magnetic field are performed. The magnetohydrodynamics (MHD for short) equations are solved numerically, in parallel with an advection-diffusion equation for the passive scalar, using a spectral resolution 3 of 256Fourier modes. The Magnetic Reynolds number is assumed to be lower than unity, so that the quasi-static approximation can be used. Turbulence statistics are computed to study the anisotropy induced by the magnetic field in the flow as well as in the scalar distribution.
INTRODUCTIONThe purpose of this work is to analyze how those flow modifications affect the transport of passive scalar quantities which can be the temperature of the medium or a pollutant density depending on Conducting fluids are encountered in many in-the application considered. dustrial and technological applications, from the fabrication of semi-conductors crystals to the de-sign of efficient cooling blankets for future fusion BASICEQUATIONS reactors (tokamaks). For most laboratory flows, the magnetic Reynolds numberRm=U L/η is very low (hereηis the magnetic diffusivity The evolution of the scalar in a flow is gov-whileUandLrepresent characteristic velocity erned by an advection-diffusion partial differen-and length scales for the flow considered). In tial equation : that case, an applied magnetic field can strongly affect the fluid's motion but there is practically no retroaction of the flow on the applied field.Θ(x, t) + (u∙ ∇)Θ(x, t) =κΔΘ(x, t)(1) ∂t This regime of magnetohydrodynamics is gov-erned by the so-called quasi-static approximation (or inductionless approximation) [1](see below).whereΘis the scalar quantity,uthe velocity field The main effects of an applied magnetic fieldandκthe diffusion coefficient. As is clear from on this kind of flows are the damping of turbu-the above equation, the transport is not directly lence through Joule dissipation and the creationaffected by the applied magnetic field but is only of anisotropy which manifest itself by the elon-modified through the damping and deformation gation of flow structures in the direction of theof the velocity field. In order to obtain the evo-magnetic field [2–5].lution ofΘ, Eq. (1) must be solved along the