Mean B-field Effects on Jet Formation in the β-Plane Magnetohydrodynamics Turbulence in the Solar Tachocline

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.