The dynamics of solar tachocline is of importance in the solar magnetic activity; the underlying physics of tachocline dynamics, however, remains unclear. Studies of tachocline have shown that the nonlinear interaction of Rossby waves— a process of inhomogeneous mixing of potential vorticity (PV)— forms a zonal jet, while a mean toroidal magnetic field (B-field) suppresses the zonal flow with a critical parameter proportional to B2/η, where η is the magnetic diffusivity (Tobias et al. 2007). Thus, the role of toroidal B-field is of significance in turbulence properties of the tachocline. As a simple model of an incompressible and stably stratified tachocline, we consider a rotating, two-dimensional model— β-plane— and examine the effect of a mean B-field on the PV mixing in the β-plane turbulence. We report an analytical theory of jet suppression due to the mean B-field, which also enters as a modification of the cross phase in the vorticity flux, and as an initiator for a flow along the tiled field lines. A mean field equation for the vorticity and comparisons of real-space and k-space formulations will also be presented by using closure and quasi-linear approximations. *This work is supported by the U.S. Department of Energy under Award No. DE-FG02-04ER54738.

Abstract The theory of turbulent transport of parallel momentum and ion heat by the interaction of stochastic magnetic fields and turbulence is presented. Attention is focused on determining the kinetic stress and the compressive energy flux. A critical parameter is identified as the ratio of the turbulent scattering rate to the rate of parallel acoustic dispersion. For the parameter large, the kinetic stress takes the form of a viscous stress. For the parameter small, the quasilinear residual stress is recovered. In practice, the viscous stress is the relevant form, and the quasilinear limit is not observable. This is the principal prediction of this paper. A simple physical picture is developed and shown to recover the results of the detailed analysis.

Tangled magnetic fields, often coexisting with an ordered mean field, have a major impact on turbulence and momentum transport in many plasmas, including those found in the solar tachocline and magnetic confinement devices. We present a novel mean field theory of potential vorticity mixing in $\beta$-plane magnetohydrodynamic (MHD) and drift wave turbulence. Our results show that mean-square stochastic fields strongly reduce Reynolds stress coherence. This decoherence of potential vorticity flux due to stochastic field scattering leads to suppression of momentum transport and zonal flow formation. A simple calculation suggests that the breaking of the shear-eddy tilting feedback loop by stochastic fields is the key underlying physics mechanism. A dimensionless parameter that quantifies the increment in power threshold is identified and used to assess the impact of stochastic field on the L-H transition. We discuss a model of stochastic fields as a resisto-elastic network.

Abstract The mean E × B shear in a stochastic magnetic field is calculated, using the radial force balance relation and transport equations. This analysis is relevant to the L → H transition with resonant magnetic perturbations, and special focus is placed upon the physics of non-ambipolar transport and radial current. The key physical process is the flow of fluctuating currents along wandering magnetic fields. The increments in poloidal and toroidal rotation, density and ion pressure are calculated. The radial envelope of the magnetic perturbations inside the plasma defines a new scale ℓ env , which is the characteristic scale of the magnetic fluctuation intensity profile. The net particle outflow due to stochastic magnetic fields is calculated and is determined by the net radial current through the separatrix. Implications for the L → H transition are discussed.