One of the key issues of stellar evolution theory is the influence of transport processes related to macroscopic motions driven by rotation on the internal structure and evolution of stars. In particular, turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is currently taken into account in many stellar evolution codes as a diffusive process whose coefficient is determined from phenomenological arguments. The purpose of this thesis is to constrain one of these coefficients, the radial diffusion coefficient driven by radial differential rotation through local direct numerical simulations describing turbulent motions induced by a locally forced shear in a stellar radiative zone. The exploration of the domain of very large thermal diffusivities -- or equivalently of small Péclet numbers -- typical of stellar interiors was made possible thanks to a suitable asymptotic expansion of the Boussinesq equations. The main result of this thesis is that our numerical simulations are in agreement with the form of the vertical turbulent diffusion coefficient proposed by J.-P. Zahn in the regime of turbulent Péclet numbers smaller than one. The results obtained for Péclet numbers greater than one are in agreement with the model of Lindborg & Brethouwer (2008) proposed in a geophysical context. The simulations taking into account the dynamical effect of chemical stratification also allowed us to validate one of the models used in stellar evolution codes and to eliminate another one.
