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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.