Consistent Theory of Turbulent Transport in Two-Dimensional Magnetohydrodynamics

A theory of turbulent transport is presented in two-dimensional magnetohydrodynamics with background shear and magnetic fields. We provide theoretical predictions for the transport of magnetic flux, momentum, and particles and turbulent intensities, which show stronger reduction compared with the hydrodynamic case, with different dependences on shearing rate, magnetic field, and values of viscosity, Ohmic diffusion, and particle diffusivity. In particular, particle transport is more severely suppressed than momentum transport, effectively leading to a more efficient momentum transport. The role of magnetic fields in quenching transport without altering the amplitude of flow velocity and in inhibiting the generation of shear flows is elucidated. Implications of the results are discussed.

Figure 1

(a) $I_1$ (solid line), $I_2$ (dotted line), $I_3$ (dashed line), $I_4/10$ (dash-dotted line), and $I_5$ (dash-dot-dot-dotted line) plotted as a function of $\alpha =B^2/\eta \Omega$ for ${\xi }_{\nu }={\xi }_D={10}^{-3}$; (b) Cross-phase $\cos \delta$ plotted as a function of $\alpha$ for ${\xi }_D={10}^{-5}$ (solid line), ${10}^{-4}$ (dotted line), and ${10}^{-3}$ (dashed line).