We examine the scaling of the two-point correlation function for $\unicode[STIX]{x1D716}$ , the energy dissipation rate, over a range of values of the separation $r$ between the two points and the Taylor microscale Reynolds number $Re_{\unicode[STIX]{x1D706}}$ . The correlation function is estimated from hot-wire measurements in grid turbulence, along the axes of wakes and jets, and along the centreline of a fully developed channel flow. When $Re_{\unicode[STIX]{x1D706}}$ exceeds a value of approximately 300, a condition which is achieved for both plane and circular jets, the correlation function collapses over nearly all values of $r$ when the normalization uses Kolmogorov scales. However, there is no collapse in either the power-law range or dissipative range when the normalization is on the integral (or external) length scale, which indicates that there is no self-similarity based on external scales. Although the maximum value of $Re_{\unicode[STIX]{x1D706}}$ is not much larger than $10^{3}$ , the behaviour of the energy dissipation correlation function on the axes of plane and circular jets seems consistent with the first similarity hypothesis of Kolmogorov ( Dokl. Akad. Nauk SSSR , vol. 30, 1941, pp. 299–303) but not with the revised phenomenology of Kolmogorov ( J. Fluid Mech. , vol. 13, 1962, pp. 82–85).

中文翻译：

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湍流能量耗散相关函数的标度

我们检查了 $\unicode[STIX]{x1D716}$ 的两点相关函数的缩放，能量耗散率，在两点之间的间隔 $r$ 和泰勒微尺度雷诺数 $ Re_{\unicode[STIX]{x1D706}}$ 。相关函数是根据网格湍流中的热线测量值估计的，沿着尾流和射流的轴，以及沿着完全发展的通道流的中心线。当 $Re_{\unicode[STIX]{x1D706}}$ 超过大约 300 的值时（平面和圆形射流都可以达到的条件），当归一化使用 Kolmogorov 时，相关函数在几乎所有 $r$ 值上都崩溃秤。然而，当归一化在积分（或外部）长度尺度上时，幂律范围或耗散范围都没有崩溃，这表明没有基于外部尺度的自相似性。尽管 $Re_{\unicode[STIX]{x1D706}}$ 的最大值并不比 $10^{3}$ 大多少，但能量耗散相关函数在平面和圆形射流轴上的行为似乎与Kolmogorov 的第一个相似性假设 (Dokl. Akad. Nauk SSSR, vol. 30, 1941, pp. 299–303) 但不是 Kolmogorov 的修正现象学 (J. Fluid Mech., vol. 13, 1962, pp. 82– 85）。