Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence.
Steep Cliffs and Saturated Exponents in Three-Dimensional Scalar Turbulence.
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DOI：
10.1103/physrevlett.121.264501
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发表时间：
2018-07
影响因子：
8.6
通讯作者：
K. Iyer;Jörg Schumacher;Jörg Schumacher;K. Sreenivasan;K. Sreenivasan;P. Yeung
中科院分区：
文献类型：
--
作者：
K. Iyer;Jörg Schumacher;Jörg Schumacher;K. Sreenivasan;K. Sreenivasan;P. Yeung
在4096^{3}网格上，采用直接数值模拟方法，研究了泰勒尺度雷诺数为650时，三维Navier-Stokes湍流中被动标量平流的湍流度，其中施密特数为1.通过测量高阶的标量增量矩，同时确保统计收敛，我们提供了明确的证据表明，标度指数饱和到1.2的时刻订单超过约12，表明标量不稳定性占主导地位的最奇异的shocklike悬崖的标量场。我们发现，陡峭的悬崖的空间支持的分形维数约为1.8，其与饱和指数值为1.2的总和加起来的空间维数为3，从而展示了湍流标量混合的几何和统计之间的深刻联系。异常的四阶和六阶矩是可比的Kraichnan模型的粗糙度指数为4/3。
The intermittency of a passive scalar advected by three-dimensional Navier-Stokes turbulence at a Taylor-scale Reynolds number of 650 is studied using direct numerical simulations on a 4096^{3} grid; the Schmidt number is unity. By measuring scalar increment moments of high orders, while ensuring statistical convergence, we provide unambiguous evidence that the scaling exponents saturate to 1.2 for moment orders beyond about 12, indicating that scalar intermittency is dominated by the most singular shocklike cliffs in the scalar field. We show that the fractal dimension of the spatial support of steep cliffs is about 1.8, whose sum with the saturation exponent value of 1.2 adds up to the space dimension of 3, thus demonstrating a deep connection between the geometry and statistics in turbulent scalar mixing. The anomaly for the fourth and sixth order moments is comparable to that in the Kraichnan model for the roughness exponent of 4/3.