CONDITIONAL SCALAR DISSIPATION RATES IN TURBULENT WAKES, JETS, AND BOUNDARY-LAYERS

The expected value E(c)hi=E(chi,theta=theta(0)) of the dissipation rat e chi of a passive scalar theta conditioned on the scalar value theta= theta(0) has been measured in three varieties of turbulent shear flows : heated wakes, dyed liquid jets, and the atmospheric surface layer. T he quantity E(chi) depends fairly strongly on theta(0) and on the flow . For the wake, E(chi) exhibits two peaks-one on the low-temperature e nd and the other on the high-temperature end-and the peaks are separat ed by an approximately flat region. The relative strength of the two p eaks varies with the spatial position. Measured in the turbulent part alone, E(chi) tends to have only one peak on the hot side, but is stil l nonuniform. The related quantity, E(theta'') = (del(2) theta,theta = theta(0)), which is the expected value of the Laplacian of the scalar conditioned on the scalar concentration, has also been measured on th e wake centerline and shows a simpler dependence on theta(0) than E(ch i). For jets, E(chi) has a single peak on the high-concentration side. This feature appears to be essentially independent of the use of Tayl or's hypothesis and on whether or not the dissipation rate chi is appr oximated by only one of its components. It is, however, sensitive to t he resolution of measurement. For the temperature fluctuation in the a tmospheric boundary layer, the peak in E(chi) 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 E(chi) 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 th e finest scales of the scalar are resolved.