Mixing and Transport in Stars

Extract

Transport and mixing in stars is as important as it is difficult to quantify (Zahn 1992; Schatzman 1996; Maeder 1997; Pinsonneault 1997). A first difficulty is that both transport and mixing are dynamical processes which, given the low viscosities of stellar interiors, usually means that the flow is turbulent giving rise to technical difficulties for turbulence is still an incomplete chapter though recent studies have brought about considerable progress. A second difficulty is that turbulence is not self-sustaining and unless there is a source, dynamical mixing and transport will decay in time and eventually die out. Thus, the question: what is the source of turbulence, let alone how to describe it? In the convective zone, the source is the unstable stratification but the mixing there is so strong that one does not need a sophisticated theory to describe it. Strong turbulence is easier to describe than weak turbulence and yet the latter is when the problems become interesting and our descriptive power is less reliable. For example, below the solar CZ we don’t even know for sure the source of stirring, let alone how to describe it and yet, it is the region where we would like to be confident about models. The transport of Li is the best example of a mixing and transport that cannot be too strong or too weak (Schlattl and Weiss 1999). A third difficulty is the unstated assumption that “transport” (advection) and “mixing” (diffusion) have different origin.