Stellar hydrodynamics in radiative regions

We present an analysis of the response of a radiative region to waves generated by a convective region of the star; this wave treatment of the classical problem of "overshooting" gives extra mixing relative to the treatment traditionally used in stellar evolutionary codes. The interface between convectively stable and unstable regions is dynamic and nonspherical, so that the nonturbulent material is driven into motion, even in the absence of "penetrative overshoot." These motions may be described by the theory of nonspherical stellar pulsations and are related to motion measured by helioseismology. Multidimensional numerical simulations of convective flow show puzzling features, which we explain by this simplified physical model. Gravity waves generated at the interface are dissipated, resulting in slow circulation and mixing seen outside the formal convection zone. The approach may be extended to deal with rotation and composition gradients ("semiconvection"). Tests of this description in the stellar evolution code TYCHO produce carbon stars on the asymptotic giant branch (AGB), an isochrone age for the Hyades and three young clusters with lithium depletion ages from brown dwarfs, and lithium and beryllium depletion consistent with observations of the Hyades and Pleiades, all without tuning parameters. The potential insight into the different contributions of rotational and hydrodynamic mixing processes could have important implications for realistic simulation of supernovae and other questions in stellar evolution.