湍流中大尺度的动力学与统计性质

中文摘要 AI 辅助

我们综述了湍流中大于强迫尺度的大尺度性质的研究结果。在三维湍流中，当驱动流动的功率在明确尺度上注入时，注入尺度将小尺度范围（其中发生Kolmogorov级联）与平均能量通量为零的大尺度范围分隔开来，表明这些模态处于平衡状态。我们表明，在仅涉及少数模态的空间周期性强迫情况下，大尺度上产生均分能量谱，并讨论了在更复杂强迫下观察到的与均分的偏差。在二维湍流中，注入尺度将直接涡度级联（向小尺度）与逆能量级联（向大尺度）分隔开来。由于逆级联的存在，人们不会预期平衡统计物理工具适用于描述大尺度结构。然而，恰恰是在这种情况下，这些工具得到了最广泛的应用。我们确实表明，在实验和直接数值模拟中观察到的二维湍流不同大尺度状态之间的分岔，可以用截断欧拉方程定性描述，其解满足统计平衡。

英文摘要

We present a review of results concerning the properties of scales larger than the forcing scale in turbulent flows. In three-dimensional turbulence, when the power driving the flow is injected at a well-defined scale, the injection scale separates the small-scale range, where the Kolmogorov cascade takes place, from the large-scale range across which the mean energy flux is zero, suggesting that these modes are in equilibrium. We show that, in the case of spatially periodic forcing involving only a few modes, an equipartition energy spectrum is generated at large scales, and we discuss the deviations from equipartition observed with more complex forcings. In two-dimensional turbulence, the injection scale separates the direct enstrophy cascade toward small scales from the inverse energy cascade toward large scales. Because of the inverse cascade, one would not expect equilibrium statistical physics tools to be suitable for describing the large-scale structures. Yet this is precisely the situation in which such tools have been most widely used. We indeed show that the bifurcations observed between different largescale regimes of two-dimensional turbulence, both in experiments and in direct numerical simulations, can be qualitatively described by the Truncated Euler equations, whose solutions satisfy statistical equilibrium.

发表机构

• Laboratoire de Physique de l’Ecole Normale Supérieure, CNRS, PSL Research University, Sorbonne Université, Université Paris Cité（巴黎高等师范学院物理实验室，法国国家科学研究中心，PSL研究大学，索邦大学，巴黎西岱大学）

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DOI

10.1098/rsta.2025.0034