The expected value E_χ≡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 E_χ depends fairly strongly on θ₀ and on the flow. For the wake, E_χ 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, E_χ 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, E_χ 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 χ 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 E_χ 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_χ 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.

中文翻译：

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湍流，水流和边界层中的条件标量耗散率

预期值ê _χ＆equiv; è（χ，θ=θ ₀的无源标量的耗散率χ的）θ调节的标量值θ=θ ₀一直被测 在三个品种中 湍流的 剪切流量： 加热的苏醒，染色 液体喷射器 和大气 表面层。数量é _χ相当强烈依赖于θ ₀和上流。对于唤醒，ê _χ具有两个峰，一个在低温端，另一对高温端和所述峰由大致平坦的区域分离。两个峰的相对强度随空间位置而变化。实测 在里面 湍流的单独的部分，ê _χ倾向于在热端只有一个高峰，但仍是不均匀的。相关的数量，ē _θ'≡（∇ ² θ，θ=θ ₀），这是标量调节标量浓度的拉普拉斯算子的预期值，也已经被测关于唤醒中心线和示出了更简单的对θ的依赖₀比ë _χ。对于喷气式飞机 È _χ对高浓度侧的单峰。该特征似乎基本上与泰勒假设的使用以及耗散率χ是否仅由其分量之一近似无关。但是，它对于以下问题很敏感：测量。 对于温度波动 大气边界层在高峰é _χ的冷端是远弱于在热侧。从实验这个组合，有人认为，不同形状é _χ不同流 与标量pdf本身的性质差异以及水中的高Schmidt数染料有关 流动 关于是否解决了标量的最佳比例的问题。