Turbulent transport and equilibrium profiles in two-dimensional magnetohydrodynamics with background shear

Turbulent transport and equilibrium profile are studied in two-dimensional magnetohydrodynamics (2D MHD) in the presence of a background shear flow an d a large-scale magnetic field; the latter quantities are assumed to be par allel and to vary in the perpendicular direction. The nonuniformity of the background is incorporated, to first order, by using the Gabor transform. T he magnetic vector potential and momentum fluxes (or total stress) are calc ulated in both kinematic and dynamic cases in the case of unit magnetic Pra ndtl number, which then determines turbulent diffusivity and viscosity and equilibrium profile of the mean shear flow. The turbulent diffusion is foun d to be suppressed for a strong (large-scale) magnetic field. The Lorentz f orce changes the sign of the total stress resulting in the turbulent viscos ity with an opposite sign compared to that in the hydrodynamical case. The former reduces the amplitude of the total stress for a fixed shear due to t he cancellation between Reynolds and Maxwell stresses, therefore leading to the reduction in momentum transport. Since the divergence of momentum flux acts as an effective force on the background shear, the presence of the ma gnetic field can lead to an equilibrium shear profile which is different fr om that of the pure hydrodynamic case. In particular, the Lorentz force is shown to laminarize the mean shear flow. (C) 2001 American Institute of Phy sics.