Mathematical reformulation of the Kolmogorov?Richardson energy cascade in terms of vortex stretching
Mathematical reformulation of the Kolmogorov?Richardson energy cascade in terms of vortex stretching
复制标题
柯尔莫哥洛夫?理查森能量级联在涡旋拉伸方面的数学重构
DOI：
10.1088/1361-6544/ac4b3b
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发表时间：
2022
期刊：
影响因子：
1.7
通讯作者：
Tsuruhashi Tomonori
中科院分区：
文献类型：
--
作者：
Yoneda Tsuyoshi;Goto Susumu;Tsuruhashi Tomonori
本文借助周期域中强迫湍流的直接数值模拟，对Kolmogorov-Richardson能量叶栅的涡拉伸展进行了数学上的重新描述。通过这种描述，我们证明了如果Navier-Stokes流满足一个新的关于拟能产生率的正则性准则，则该流不会爆破。我们的DNS结果似乎支持这一规律性标准。接下来，我们从数学上构造了管状涡的层次结构，它在惯性范围内具有统计上的自相似性。在涡旋伸展/压缩(即能量级联)过程的局部尺度和非直接伸展或压缩涡旋之间的统计独立性的假设下，我们可以导出统计定常湍流能谱的−5/3幂定律，而不直接使用科尔莫戈罗夫假设。
In this paper, with the aid of direct numerical simulations (DNS) of forced turbulence in a periodic domain, we mathematically reformulate the Kolmogorov–Richardson energy cascade in terms of vortex stretching. By using the description, we prove that if the Navier–Stokes flow satisfies a new regularity criterion in terms of the enstrophy production rate, then the flow does not blow up. Our DNS results seem to support this regularity criterion. Next, we mathematically construct the hierarchy of tubular vortices, which is statistically self-similar in the inertial range. Under the assumptions of the scale-locally of the vortex stretching/compressing (ie energy cascade) process and the statistical independence between vortices that are not directly stretched or compressed, we can derive the− 5/3 power law of the energy spectrum of statistically stationary turbulence without directly using the Kolmogorov hypotheses.