Rain and clouds in brown dwarf atmospheres: a coupled problem from small to large

The large scale structure of a brown dwarf atmosphere is determined by an interplay of convection, radiation, dust formation, and gravitational settling, which possibly provides an explanation for the observed variability. The result is an element depletion of the dust forming regions and an element enrichment of the dust evaporating sites. The formation of dust cloud structures in substellar atmospheres is demonstrated based on a consistent theoretical description of dust formation and destruction, gravitational settling, and element depletion including the effect of convective overshoot. Since the viscosity is small in brown dwarf atmospheres, the convection creates a turbulent environment with fluctuations of all thermodynamic state variables on a wide range of spatial scales. Hence, the classical turbulent closure problem needs to be tackled in connection with dust formation in substellar objects, because a complete three-dimensional and time-dependent solution of the model equations is simply not possible. Structure formation may be seeded on the smallest scales, when chemical processes are involved. In order to understand the interaction of turbulence and dust formation, we have performed investigations of the smallest scale regimes in 1D and in 2D in order to identify the governing processes of the unresolved scale regime.