We present a local but fully nonlinear model of the solar tachocline, using three-dimensional direct numerical simulations. The tachocline forms naturally as a statistically steady balance between Coriolis, pressure, buoyancy and Lorentz forces beneath a turbulent convection zone. Uniform rotation is maintained in the radiation zone by a primordial magnetic field, which is confined by meridional flows in the tachocline and convection zone. Such balanced dynamics has previously been found in idealised laminar models, but never in fully self-consistent numerical simulations.

Motivated by the dynamics in the deep interiors of many stars, we study the interaction between overshooting convection and the large-scale poloidal fields residing in radiative zones. We have run a suite of 3D Boussinesq numerical calculations in a spherical shell that consists of a convection zone with an underlying stable region that initially compactly contains a dipole field. By varying the strength of the convective driving, we find that, in the less turbulent regime, convection acts as turbulent diffusion that removes the field faster than solely molecular diffusion would do. However, in the more turbulent regime, turbulent pumping becomes more efficient and partially counteracts turbulent diffusion, leading to a local accumulation of the field below the overshoot region. These simulations suggest that dipole fields might be confined in underlying stable regions by highly turbulent convective motions at stellar parameters. The confinement is of large-scale field in an average sense and we show that it is reasonably modeled by mean-field ideas. Our findings are particularly interesting for certain models of the Sun, which require a large-scale, poloidal magnetic field to be confined in the solar radiative zone in order to explain simultaneously the uniform rotation of the latter and the thinness of the solar tachocline.