The expected value Eχ≡E(χ,θ= θ0) of the dissipation rate χ of a passive scalar θ conditioned on the scalar value θ = θ0 has been measured in three varieties of turbulent shear flows: heated wakes, dyed liquid jets, and the atmospheric surface layer. The quantity Eχ depends fairly strongly on θ0 and on the flow. For the wake, Eχ exhibits two peaks - one on the low-temperature end and the other on the high-temperature end - and the peaks are separated by an approximately flat region. The relative strength of the two peaks varies with the spatial position. Measured in the turbulent part alone, Eχ tends to have only one peak on the hot side, but is still nonuniform. The related quantity, E θ″=(∇2θ,θ= θ0), which is the expected value of the Laplacian of the scalar conditioned on the scalar concentration, has also been measured on the wake centerline and shows a simpler dependence on θ0 than E χ- For jets, Eχ has a single peak on the high-concentration side. This feature appears to be essentially independent of the use of Taylor's hypothesis and on whether or not the dissipation rate ψ is approximated by only one of its components. It is, however, sensitive to the resolution of measurement. For the temperature fluctuation in the atmospheric boundary layer, the peak in Eχ on the cold side is far weaker than that on the hot side. From this combination of experiments, it is argued that the different shapes of Eχ in different flows are related to differences in the nature of the scalar pdf itself and, for the high-Schmidt-number dyes in water flows, on whether or not the finest scales of the scalar are resolved.
ASJC Scopus subject areas