Tsuruhashi Tomonori, Goto Susumu, Oka Sunao, Yoneda Tsuyoshi
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan.
Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan.
Philos Trans A Math Phys Eng Sci. 2022 Jun 27;380(2226):20210053. doi: 10.1098/rsta.2021.0053. Epub 2022 May 9.
Energy transfers from larger to smaller scales in turbulence. This energy cascade is a process of the creation of smaller-scale coherent vortices by larger ones. In our recent study (Yoneda, Goto and Tsuruhashi 2022 , 1380-1401), we reformulated the energy cascade in terms of this stretching process and derived the [Formula: see text] law of the energy spectrum under physically reasonable assumptions. In the present study, we provide a quantitative verification of these assumptions by using direct numerical simulations. We decompose developed turbulence in a periodic cube into scales by using the band-pass filter and identify the axes of coherent tubular vortices by the low-pressure method. Even when the turbulent kinetic energy and its dissipation rate temporally fluctuate about their temporal means, the total length of the vortices at each scale varies little with time. This result is consistent with our assumption of the temporal stationarity on the vorticity decomposition. The present numerical analysis also shows that the hierarchy of vortex axes is self-similar in a wide range of scales, i.e. in the inertial range and a lower part of the dissipation range and that the volume fraction occupied by the tubular vortices at each scale is independent of the scale. This article is part of the theme issue 'Mathematical problems in physical fluid dynamics (part 2)'.
在湍流中，能量从较大尺度传递到较小尺度。这种能量级串是一个由较大涡旋产生较小尺度相干涡旋的过程。在我们最近的研究（米田、后藤和鹤桥，2022 年，第1380 - 1401页）中，我们根据这种拉伸过程重新阐述了能量级串，并在物理上合理的假设下推导出了能谱的[公式：见正文]定律。在本研究中，我们通过直接数值模拟对这些假设进行了定量验证。我们使用带通滤波器将周期性立方体中发展成熟的湍流按尺度分解，并通过低压法确定相干管状涡旋的轴。即使湍动能及其耗散率随时间围绕其时间平均值波动，每个尺度上涡旋的总长度随时间变化很小。这一结果与我们在涡度分解上的时间平稳性假设一致。本数值分析还表明，在广泛的尺度范围内，即惯性范围和耗散范围的较低部分，涡旋轴的层次结构是自相似的，并且每个尺度上管状涡旋所占的体积分数与尺度无关。本文是主题特刊“物理流体动力学中的数学问题（第二部分）”的一部分。
