Horizontal turbulent transport in stars : progresses and challenges

In his seminal work on the transport of angular momentum and chemicals in stellar radiation zones (Zahn 1992), Jean-Paul Zahn proposed a coherent and complete formalism based on the hypothesis of a strong anisotropic turbulent transport stronger in the horizontal direction because of the stable stratification of these regions. This allowed him to derive equations to describe the evolution of rotating stars in a formalism that assumes the so-called « shellular » rotation, where the rotation mostly varies along the radial direction. This coherent theory, often called rotational mixing, has been broadly and successfully implemented in stellar evolution codes and applied to many types of stars.

However, very few prescriptions (at least three) have been proposed in the literature for the turbulent transport in the horizontal direction. Moreover, while based on the hypothesis of an anisotropy of turbulent transport induced by stable stratification in rotating radiation zones, none of them have an explicit dependence on the buoyancy frequency neither rotation. In addition, the resulting predictions are unable to reproduce the weak differential rotation observed in the Sun and stars thanks to helio- and asteroseismology.

In this context, understanding properties of turbulent transport in rotating stratified fluids is at the forefront of fundamental fluid dynamics research using theory, numerical simulations and laboratory experiments. In this seminar, based on last advances in the field, I will show how new prescriptions for the anisotropy of transport and related horizontal eddy diffusion coefficient that have an explicit dependence on stratification, rotation, and thermal diffusion can be derived.

One of these new prescriptions has been implemented in a stellar evolution code and applications to solar-type stars’ evolution from their PMS to advanced stages of evolution have been computed. Obtained results show a potentially stronger but self-regulated turbulent transport that should be taken into account but cannot reproduce the observed rotation profiles.

These results will be discussed in the general context of on-going progresses for the theory, the modelling, and numerical simulations of hydrodynamic and magneto-hydrodynamic mechanisms that transport angular momentum in stellar interiors and of the confrontation of their predictions to seismic constrains on their rotation.