  Just as correlations between fluctuating radial and azimuthal velocities
produce a coherent stress contributing to the angular momentum transport in
turbulent accretion disks, correlations in the velocity and temperature
fluctuations produce a coherent energy flux. This nonadvective energy flux is
always of secondary importance in thin radiative disks, but cannot be neglected
in nonradiative flows, in which it completes the mean field description of
turbulence. It is, nevertheless, generally ignored in accretion flow theory,
with the exception of models explicitly driven by thermal convection, where it
is modeled phenomenologically. This flux embodies both turbulent thermal
convection as well as wave transport, and its presence is essential for a
proper formulation of energy conservation, whether convection is present or
not. The sign of the thermal flux is likely to be outward in real systems, but
the restrictive assumptions used in numerical simulations may lead to inward
thermal transport, in which case qualitatively new effects may be exhibited. We
find, for example, that a static solution would require inward, not outward,
thermal transport. Even if it were present, thermal convection would be
unlikely to stifle accretion, but would simply add to the outward rotational
energy flux that must already be present.
