  The effects of a non-gradient flux term originating from the motion of
convective elements with entropy perturbations of either sign are investigated
and incorporated into a modified version of stellar mixing length theory (MLT).
Such a term, first studied by Deardorff in the meteorological context, might
represent the effects of cold intense downdrafts caused by the rapid cooling in
the granulation layer at the top of the convection zone of late-type stars.
Such intense downdrafts were first seen in the strongly stratified simulations
of Stein & Nordlund in the late 1980s. These downdrafts transport heat
nonlocally, a phenomenon referred to as entropy rain. Moreover, the Deardorff
term can cause upward enthalpy transport even in a weakly Schwarzschild-stably
stratified layer. In that case, no giant cell convection would be excited. This
is interest in view of recent observations, which could be explained if the
dominant flow structures were of small scale even at larger depths. To study
this possibility, three distinct flow structures are examined: one in which
convective structures have similar size and mutual separation at all depths,
one in which the separation increases with depth, but their size is still
unchanged, and one in which both size and separation increase with depth, which
is the standard flow structure. It is concluded that the third possibility with
fewer and thicker downdrafts in deeper layers remains most plausible, but it
may be unable to explain the suspected absence of large-scale flows with speeds
and scales expected from MLT.
