The small-Péclet-number approximation in stellar radiative zones

We present an asymptotic form of the Boussinesq equations in the limit of small Péclet numbers i.e. when the time scale of motions is much larger than the time scale of thermal diffusion. We find that, in this limit, the effects of thermal diffusion and stable stratification combine in a single physical process. This process is an anisotropic dissipation (not effective for horizontal motions) which acts primarily on large scale motions. The small-Péclet-number approximation presents also the great practical interest to avoid the numerical difficulty induced by the huge separation between the diffusive and dynamical time scales. The relevance of this approximation to study the flow dynamics within the stellar radiative zones is considered.