Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal
Circulation in High Reynolds Number Isotropic Turbulence is a Bifractal
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DOI：
10.1103/physrevx.9.041006
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发表时间：
2019-02
影响因子：
12.5
通讯作者：
K. Iyer;K. Sreenivasan;P. Yeung
中科院分区：
文献类型：
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作者：
K. Iyer;K. Sreenivasan;P. Yeung
在标度指数水平上的湍流问题是困难的，部分原因是由于小尺度的多重分形标度，这要求对每个矩阶进行独立的处理和理解。这一结论来源于对速度结构函数、能量耗散、熵密度（即涡量的平方）等方面的研究。然而，在惯性范围内，很可能存在其他物理上相关的、结构不复杂的物理量，这可能会导致湍流理论的巨大简化。我们证明了环绕闭环的速度循环就是这样一个量。通过使用各向同性湍流的大型数据库，在广泛的雷诺数范围内对Navier-Stokes方程进行数值模拟，我们表明，在考虑的最高雷诺数下，循环表现出一种分形行为：在3阶矩处的空间填充，在高阶矩处的单分形，维数不变，约为2.5阶；这种大致发生在三阶时刻的特征变化让人联想到“相变”。我们探索的可能性，循环成为有效的空间填充在高得多的雷诺数，即使它可能在技术上被视为分岔。我们确认循环特性只取决于环路的面积，而不是它的形状；对于数字$8的循环，相关的面积是循环的两段的标量和。
The turbulence problem at the level of scaling exponents is hard in part because of the multifractal scaling of small scales, which demands that each moment order be treated and understood independently. This conclusion derives from studies of velocity structure functions, energy dissipation, enstrophy density (that is, square of vorticity), etc. However, it is likely that there exist other physically pertinent quantities with uncomplicated structure in the inertial range, potentially resulting in huge simplifications in the turbulence theory. We show that velocity circulation around closed loops is such a quantity. By using a large databases of isotropic turbulence, generated from numerical simulations of the Navier-Stokes equations over a wide range of Reynolds numbers, we show that circulation exhibits a bifractal behavior at the highest Reynolds number considered: space filling for moments up to order $3$ and a mono-fractal with an unchanging dimension of about $2.5$ for higher orders; this change in character roughly at the third-order moment is reminiscent of a "phase transition". We explore the possibility that circulation becomes effectively space filling at much higher Reynolds numbers even though it may technically be regarded as a bifractal. We confirm that the circulation properties depend on only the area of the loop, not its shape; and, for a figure-$8$ loop, the relevant area is the scalar sum of the two segments of the loop.