Direct numerical simulations of the velocity and temperature fields for turbulent flow
in a channel are used to examine the influence of Prandtl number Pr on turbulent
transport. The Reynolds number, based on the half-height of the channel and the
friction velocity, is Reτ = 150. Prandtl numbers of 1.0, 0.3, 0.1, 0.05, 0.025 were
studied. The bottom and the top walls were kept at constant temperatures of +Tw
and −Tw. The influence of Pr on Reynolds transport, on the turbulent diffusivity, ατ,
and on the spectral density function of the temperature fluctuations was studied. The
observation that spatial variations of the ratio of the turbulent diffusivity to the value
observed at Pr = 1.0 are not large is used to propose a method for calculating average
temperature fields. The decrease in ατ with decreasing Pr is related to observations
of the increased damping of high-wavenumber temperature fluctuations. Molecular
conductivity, at smaller Pr, is pictured to act as a filter that renders high-frequency
velocity fluctuations ineffective in transporting heat.