Douglas Gough & Michael McIntyre proposed, in 1998, the first global and self-consistent model of the solar tachocline. Their model is however far more complex than analytical methods can deal with. In order to validate their work and show how well it can indeed represent the tachocline dynamics, I report on progress in the construction of a fully nonlinear numerical model of the tachocline based on their idea. Two separate and complementary approaches of this study are presented: the study of shear propagation into a rotating stratified radiative zone, and the study of the nonlinear interaction between shear and large-scale magnetic fields in an incompressible, rotating sphere. The combination of these two approaches provides good insight into the dynamics of the tachocline.

Introduction

The tachocline was discovered in 1989 by Brown et al.; it is a thin shear layer located at the interface of the uniformly rotating radiative zone and differentially rotating convective zone of the sun. Several issues about these observations remain unclear. Why is the radiative zone rotating uniformly despite the latitudinal shear imposed by the convection zone, and why is the tachocline so thin? How can the tachocline operate the dynamical transition between the magnetically spun-down convection zone and the interior? The first model of the tachocline was presented by Spiegel & Zahn (1992).