Non-Local Convection Models for Stellar Atmospheres and Envelopes

We present an overview of the concepts underlying advanced non-local Reynolds stress models of turbulent convection and review a comparison of this approach with a series of numerical simulations of fully compressible convection. We then discuss results from applications of the model to complete envelopes of A-type main sequence stars. The non-local model reproduces surface velocities in agreement with the lower limit of observed macro- and microturbulence velocities of A-star photospheres, the asymmetry of the surface velocity field as inferred from spectral line profiles, and the overall structure of the photospheric and subphotospheric convection zones, as predicted by the most recent numerical simulations available for these stars. Traditionally, local models of convection are unable to do so. We conclude with a brief survey of extensions of the model which are interesting for other applications such as atmospheres of solar type stars and overshooting below deep convective envelopes or above the core in massive stars.