On the penetration of large-scale flows into stellar radiative zones

The propagation of meridional circulation below the base of the convection zone of low-mass stars may play a crucial role in the transport of angular momentum and also significantly contribute to the transport of chemical species and magnetic fields within their stable radiative zone. We systematically study these large-scale mean flows by performing three-dimensional (3D) global numerical simulations in a spherical shell that consists of a convection zone (CZ) overlying a stably stratified region. We find that the meridional flows can penetrate distances as large as $\sim 0.21r_o$ (where $r_o$ is the outer radius) below the base of the convection zone, provided that the Eddington-Sweet timescale $t_{ES}$ is much shorter than the viscous timescale $t_{\nu}$ as measured by the parameter $\sigma=(t_{ES}/t_{\nu})^{1/2}$. In the solar-like regime where $\sigma\lesssim 1$ in the upper radiative zone (RZ), we find that the angular momentum transport in the deep RZ is determined primarily by the action of the Coriolis force on meridional flows. In contrast, in models run in the $\sigma> 1$ regime, the meridional flows become weaker and the viscous effects dominate. We find that the penetration lengthscale $\delta_{MC}$ of these mean flows when $\sigma\lesssim 1$ is proportional to $\sigma^{-0.22}$. Our findings may provide a better understanding of the role of the meridional flows in the dynamics of the solar interior and inform future numerical studies that are focused on capturing solar-like dynamics self-consistently.