The physical processes causing the turbulent dissipation and mixing of momentum and magnetic fields in the solar tachocline are discussed in the context of a simple model of two-dimensional MHD turbulence on a β-plane. The mean turbulent resistivity and viscosity for this model are calculated. Special attention is given to the enhanced dynamical memory induced by small scale magnetic fields and to the effects of magnetic fluctuations on nonlinear energy transfer. The analogue of the Rhines scale for β-plane MHD is identified. The implications of the results for models of the solar tachocline structure are discussed.

Introduction

The tachocline is a thin, stably stratified layer of the solar interior situated in the radiative zone, immediately below the convection zone (Miesch 2005;Tobias 2005). This layer connects the latitudinal differential rotation of the solar convection zone to the expected solid body rotation of the solar interior (Schou et al. 1998; see also Chapter 3 in this book by Christensen-Dalsgaard & Thompson). Thus, flows in the tachocline are sheared (both poloidally and radially), with the predominant structure being that of a radially sheared toroidal flow. The stratification of the tachocline is strongly stable (with Richardson number Ri ≫ 1), and the magnetic field strength is significant, though magnetic pressure is still much smaller than thermal pressure, consistent with hydrostatic equilibrium, i.e. B2/8π ≪ p.