The overshoot region at the bottom of the solar convection zone

The extent and thermal stratification of the region of convective overshoot underneath the convection zone of the sun are investigated. The phenomenon of convective overshoot in general is discussed, and some of the modal and model approaches to studying it are briefly reviewed. A detailed theoretical description of the motion of plumes in a stably stratified medium is given, leading to a 'derivation' of the plume equations from the hydrodynamic equations. Entrainment is discussed, and it is shown how the plume equations can be used to compute convective overshoot in the sun. The limitations of the plume model are addressed, arguing that a thin boundary layer must exist which separates convective and radiative regions. The results of numerical integrations of the plume equations, as applied to the region of convective overshoot underneath the solar convective zone, are discussed.