Turbulent mixing in presence of gravity
Stars are believed to be formed in giant molecular clouds (GMC), which is made up of mostly molecular hydrogen and small amounts of heavier elements which we collectively call “metals”. The gravitational forces of the gas tries to concentrate density to smaller and smaller regions, a process that is resisted by gas pressure. If the mass of the gas is large enough, or the volume within which it exists is small enough an instability - Jeans instability - can develop by virtue of which the gas of the molecular cloud collapses to form a star. If the metals within GMC are well mixed within the gas then stars formed in the same neighbourhood of the GMC would have very similar chemical composition. The opposite can happen if the mixing is poor. As the molecular mixing coefficients are very small, it is the turbulence in GMC that are responsible for the mixing process. It has now been established [Melendez et al. (2009)] that the Sun has a different composition of its surface layers compared to most solar twins in the solar neighbourhood. The mechanism by which this happened -- an important clue to unravel the history of formation of the Sun -- is not yet understood; although several suggestions exist. An interesting finding along similar lines is also the recent result by Liu et al. (2016) that significant chemical abundance differences exist between stars in the nearby star cluster The Hyades. These results cast significant doubts concerning the generally made assumption in studies of the evolution of our Galaxy that the composition of solar-type stars truly reflect the (assumed homogeneous) composition of the GMC from which they once formed. We want to investigate the mixing processes in GMCs by direct numerical simulations (DNS) of the equations of evolution of gas in presence of self-gravity and turbulence. In particular, we shall calculate mixing of passive scalars (density of “metals”) by turbulent flows that are set up by self-gravity and external forces (e.g., stellar winds). The effects of dynamic decoupling between gas and dust and of existing radiation fields will also be explored.