Eddy viscosity and laminarization of sheared flow in three dimensional reduced magnetohydrodynamic turbulence

The effect of Alfvén waves on turbulent momentum transport is studied in three-dimensional reduced magnetohydrodynamic turbulence. A strong external uniform magnetic field B₀ is assumed to be present orthogonal to both background shear flow and its inhomogeneity. Energy is injected into the fluid and/or magnetic field on small scales. It is shown analytically that eddy viscosity is reduced as 1/B²₀ for a strong B₀, due to the cancellation of the Reynolds stress by Maxwell stress. The sign of eddy viscosity is found to depend on the detailed properties of forcings. Specifically, it is positive for fluid forcing but depends on the anisotropy of the forcing in the case of magnetic forcing. Furthermore, it is indicated that a magnetic field tends to laminarize a mean shear flow. The possible implication of these results for the dynamics of the zonal flows in tokamaks is discussed in view of the cancellation of stresses.