| Summary: | 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 thermal 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, for which it is modeled phenomenologically. This flux embodies both turbulent thermal convection and 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.
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