Beyond the Mixing-Length Theory: A Turbulent Diffusivity Approach

Abstract

The large eddy simulation of the turbulent convection can be reduced to different types of treatment depending on the window size which filters out smaller scale eddies. In the largest eddy limit, it is reduced in a sense to Xiong’s nonlocal mixing-length theory which is suitable for the construction of stellar convection zones. For large wave numbers the spectral theory is valid and gives correct estimates for the eddy diffusivities. The single mode simulation subject to the effective Reynolds number of about 10 is suggested from the nonlinear convection theory to simulate correct dynamics of large scale flow. However, since eddies of different sizes are segregated each other to different depths in the convection zone by means of high stratification of eddy diffusivities, the single mode simulation is also appropriate to study hydrodynamical properties in stellar convection zones.KeywordsRayleigh NumberLarge Eddy SimulationEddy ViscosityConvection ZoneEddy DiffusivityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.