Masters research project: double-diffusive instabilities in stars
In the classical stellar evolution picture, stellar interiors are divided into two types: those which are convective and those which are radiative. To find which situation you have, you simply have to use the Schwarzschild criterion, or the Ledoux criterion in the case of a non-uniform molecular weight. However, as has been observed in Earth's oceans, satisfaction of these criteria does not guarantee stability. In the oceans we see widespread occurence the "salt fingers" instability which develops warm salty water lies above cold, less salty water. This process works because salt diffuses much more slowly than heat, so that fingers of salty water moving downwards lose their heat to the surroundings but retain their excess salt, keeping them more dense than the surroundings and so continuing their downwards propagation. This is one of the most important processes in which water is mixed vertically in the oceans. Conversely, if cold fresh water lies above warmer salty water (but where the temperature and salt concentration gradients are such that normal convection does not occur), convection in layers can occur where the salt concentration becomes a step function. This occurs for instance below sheets of melting sea ice, and can be demonstrated easily in a coffee cup (milk taking the place of salt).
Both of these so-called "double diffusive" instabilties are also known to occur in stars (with various chemical elements assuming the role of salt), and should have significant effects on the evolution of star. However, neither have been studied in the stellar context and our current understanding is poor. This project would involve looking at these instabilities using both analytical tools (i.e. equations, pencil and paper) and with the aid of numerical simulations.
Some prior knowledge of fluid mechanics is desirable but not essential.