Linear analysis and nonlinear evolution of two-dimensional global magnetohydrodynamic instabilities in a diffusive tachocline

This instability has previously been studied by us and others for an idealized tachocline with no kinematic viscosity and magnetic diffusivity. Since radial diffusion is more important than latitudinal diffusion in the thin solar tachocline, diffusive decay of flow and magnetic fields can be considered as proportional to those variables.

We find that, for solar-like toroidal magnetic fields of similar to100 kG, instability exists for a wide range of kinetic and magnetic drag parameters, providing a mechanism for enhanced angular momentum transport in latitudes, which could explain how thin the solar tachocline is. From a detailed parameter space survey, we set upper limits of 5 x 10(11) and 3 x 10(10) cm(2) s(-1) for kinematic viscosity and magnetic diffusivity, respectively, such that this instability occurs in the solar tachocline on a timescale shorter than a sunspot cycle.