Aspects of the solar tachocline

The splitting of the frequencies of p-modemultiplets enables information to be gained about the internal rotation of the sun. Such data have revealed a transition at the base of the convection zone from differential rotation similar to that observed at the surface to almost solid-body rotation in the radiative interior. This transition region, known as the tachocline, has been found to be relatively narrow and centred below the base of the convection zone. In this paper, the evolution of the transition region is investigated numerically. Without a large anisotropic viscosity, the depth to which it would spread in one solar age, under the assumption of a constant prescribed differential rotation at the base of the convection zone, is found to be greater than its extent as inferred from helioseismology. In the second part of the paper a highly anisotropic turbulent viscosity with a large horizontal component, as suggested by Spiegel & Zahn (1992), is assumed. In this case, a steady tachocline is formed in which the advection of angular momentum balances the Reynolds stresses. The horizontal component of turbulent viscosity required tomatch the thickness of the tachocline to that obtained by helioseismology is estimated to be 5× 105cm2s−1. The transport of helium is studied in this case and is found to yield a sound-speed increase similar to that required by helioseismology.