Anisotropic Turbulent Diffusion In Radiative Zones Of Stars

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Transport of chemical elements in radiative zone is always an open question in the theory of stellar evolution. Up to now, the standard model which takes into account the microscopic diffusion lacks to accurately predict the abundances anomalies at the top of the main sequence stars. Since more than ten years, other processes involving turbulence and waves are under investigation. But, the mechanism by which they increase or decrease the vertical diffusion of the chemical elements to the top of the star is not yet understood. At the beginning of the 90s, Chaboyer and Zahn (1992) proposed a model of turbulent diffusion coefficients assuming no overlap between the small and large turbulent scales. This last assumption was the main failure of the model and gave clues for the next studies. Vincent, Michaud et al (1996) made 2D simulations of anisotropic turbulence and showed that the vertical transport of a passive scalar is reduced when the vortices are more stretched in the horizontal direction than in the vertical one. Our work was to find again the results of Vincent et al by solving the Navier-Stokes equations under the Boussinesq approximation. We succeeded in. But, as it is usual in science, we faced new misunderstandings. For example, we found that the vertical transport of the tracer levels off in highly anisotropic turbulent flows. This stop was announced by previous studies and demonstrated with waves processes. But in our work, the Prandtl number is low enough to efficiently damp the gravity waves. The reduction of the vertical transport and the level off are only involved by sheared turbulence.

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