Journal of Fluid Mechanics

Why, how, and when, MHD turbulence becomes two-dimensional

JoëL  Sommeria a1 and René  Moreau a1
a1 Institut de Mécanique, Université de Grenoble, B.P. 53X, 38041 Grenoble Cedex, France

Article author query
sommeria j   [Google Scholar] 
moreau r   [Google Scholar] 


A description of MHD turbulence at low magnetic Reynolds number and large interaction parameter is proposed, in which attention is focussed on the role of insulating walls perpendicular to a uniform applied magnetic field. The flow is divided in two regions: the thin Hartmann layers near the walls, and the bulk of the flow. In the latter region, a kind of electromagnetic diffusion along the magnetic field lines (a degenerate form of Alfvén waves) is displayed, which elongates the turbulent eddies in the field direction, but is not sufficient to generate a two-dimensional dynamics. However the normal derivative of velocity must be zero (to leading order) at the boundaries of the bulk region (as at a free surface), so that when the length scale l[perpendicular] perpendicular to the magnetic field is large enough, the corresponding eddies are necessarily two-dimensional. Furthermore, if l[perpendicular] is not larger than a second limit, the Hartmann braking effect is negligible and the dynamics of these eddies is described by the ordinary Navier-Stokes equations without electromagnetic forces. MHD then appears to offer a means of achieving experiments on two-dimensional turbulence, and of deducing velocity and vorticity from measurements of electric field.

(Published Online April 20 2006)
(Received May 18 1981)
(Revised October 25 1981)