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The tachocline may be subject to a variety of instabilities leading to turbulent motion and angular momentum transport. This chapter reviews some approaches that have been found useful in the study of astrophysical accretion discs and discusses their possible application to the tachocline.
The solar tachocline is a thin structure characterized by strong differential rotation, presumably in the presence of a magnetic field. It forms the interface between the radiative interior and the convective envelope of the Sun, which differ greatly in their dynamical properties, states of rotation and mechanisms of angular momentum transport. While the tachocline might have the character of a laminar boundary layer between these regions, it is more likely to be turbulent, at least in part, as a result of intrinsic instabilities or possibly because of forcing by the convective motions above.
Instabilities of the tachocline could derive from kinetic, gravitational or magnetic sources of free energy. Shear instabilities depend on the free kinetic energy in differential rotation, and may, as in the case of the magnetorotational instability, require the assistance of a magnetic field. Gravitational energy may be liberated through magnetic buoyancy (Parker) instabilities, while magnetic energy in non-potential configurations may be released in purely magnetic (Tayler) instabilities. To understand the existence and dynamics of the tachocline requires an appreciation of such instabilities and the transport effects, especially angular momentum transport, to which they give rise in a nonlinear regime.