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.