Turbulent transport in radiative zones of stars

Context. In stellar interiors, rotation is able to drive turbulent motions, and the related transport processes have a significant influence on the evolution of stars. Turbulent mixing in the radiative zones is currently taken into account in stellar evolution models through a set of diffusion coefficients that are generally poorly constrained. Aims. We want to constrain the form of one of them, the radial diffusion coefficient of chemical elements due to the turbulence driven by radial differential rotation, derived by Zahn (1974, 1992) on phenomenological grounds and largely used since. Methods. We performed local, direct numerical simulations of stably stratified homogeneous sheared turbulence using the Boussinesq approximation. The domain of low P\'eclet numbers found in stellar interiors is currently inaccessible to numerical simulations without approximation. It is explored here thanks to a suitable asymptotic form of the Boussinesq equations. The turbulent transport of a passive scalar is determined in statistical steady states. Results. We provide a first quantitative determination of the turbulent diffusion coefficient and find that the form proposed by Zahn is in good agreement with the results of the numerical simulations.