TURBULENT PLUMES IN STELLAR CONVECTIVE ENVELOPES

Recent numerical simulations of compressible convection in a stratifie d medium suggest that strong downwards directed flows may play an impo rtant role in stellar convective envelopes, both in the dynamics and i n the energy transport. We transpose this idea to stellar convective e nvelopes by assuming that these plumes are turbulent plumes which may be described by Taylor's entrainment hypothesis, whose validity is wel l established in various geophysical conditions. We consider first the ideal case of turbulent plumes occurring in an isentropic atmosphere, and ignore all types of feedback. Thereafter we include the effect of the backflow generated by the plumes, and take into account the contr ibution of the radiative flux. The main result is that plumes originat ing from the upper layers of a star are able to reach the base of its convective envelope. Their number is necessarily limited because of th eir conical shape; the backflow further reduces their number to a maxi mum of about 1000. In these plumes the flux of kinetic energy is direc ted downwards, but it is less than the upwards directed enthalpy flux, so that the plumes always carry a net energy flux towards the surface . Our plume model is not applicable near the surface, where the depart ures from adiabaticity become important due to radiative leaking; ther efore it cannot predict the depth of the convection zone, which is det ermined mainly by the transition from the radiative regime above to th e nearly adiabatic conditions below. Neither does it permit to evaluat e the extent of penetration, which strongly depends on the (unknown) n umber of plumes. We conclude that, to be complete, a phenomenological model of stellar convection must have a dual character: it should incl ude both the advective transport through diving plumes, which is outli ned in this paper, and the turbulent diffusion achieved by the interst itial medium. Only the latter process is apprehended by the familiar m ixing-length treatment.