Conditional averages in convective turbulence

Two exact results are presented for the thermal dissipation in a Rayleigh-Bénard geometry. The first result expresses the conditional dissipation at each value of θ within the entire volume of the system in terms of the thermal flux and the PDF for θ. The second gives the conditional dissipation in a region of the cell in terms of the conditional flux into the region. These results are used to argue that the observed stretched exponential PDF in the central region must be connected with the behavior near the boundary.