Transport of Heat and Matter by Convection in Stars

Abstract

A quantitative analysis of the transport of heat in thermal convection is developed. An essential improvement consists in allowing for the lateral exchange of heat between the turbulent elements. The analysis is applied to the case of a medium with an originally stable stratification by molecular weight†, and to Coriolis stratification of convection itself produced by rotation. The start of small-scale convection may be prevented by the radiative exchange of heat. Quantitative conditions of the start of convection are investigated. As compared with radiation, viscosity is an insignificant factor in impeding thermal convection. The mixing efficiency, or the transport of matter by thermal convection in a stratified medium is investigated.† The mixing efficiency is strongly influenced by rotation. At a certain limiting angular speed of rotation thermal convection may be stopped altogether. The propagation of convection in a metastable “ super-adiabatic ” layer (in which the temperature gradient exceeds the adiabatic value, but which possesses a stable stratification by molecular weight) is investigated. The process of mixing in such a layer involves time intervals of the order of $${10}^{5}-{10}^{6}$$ years, for a solar mass. The bearing of these results upon a theory of the ice ages is considered.