case western reserve university



Fully non-local models of convection: their necessity, tests with numerical simulations, and an application to A-star envelopes

Friedrich Kupka (Vienna)

Advances in both observations and theory over the last three decades have revealed the shortcomings of traditional convection models based on local stability and scale length arguments. The necessity to improve the modeling of convection stems from many different branches of astrophysics. Particular problems include temperature structure and angular momentum distribution in the sun, distribution of element abundances, helium and metal diffusion and production, life time and interior composition of massive stars, modeling of progenitors of supernovae and exotic objects, generation or modulation of stellar pulsation and magnetic fields, and many others. After an overview on astrophysical problems related to the modeling of convection we present a survey of the ideas underlying the recent, fully non-local Reynolds stress model of turbulent convection by Canuto et al. (1992-2001). We then compare this model with numerical simulations of fully compressible convection by H.J. Muthsam and explain how to select among different statistical (closure) hypotheses proposed for the Reynolds stress model. The futility of attempts to use simulations to tune closure constants of ill-fated hypotheses is shown as well.

We conclude by discussing results of our application of the Reynolds stress model to envelopes of A type main sequence stars. The non-local model allows to reproduce 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 convection zone, as obtained from numerical simulations of B. Freytag, remarkably well. Traditional, local models of convection fail to succeed in any of these problems.