ABSTRACT Understanding of the structure of turbulent flows at extreme Reynolds numbers (Re) is relevant because of several reasons: almost all turbulence theories are only valid in the high Re limit, and most turbulent flows of practical relevance are characterized by very high Re. Specific questions about wall-bounded turbulent flows at extreme Re concern the asymptotic laws of the mean velocity and turbulence statistics, their universality, the convergence of statistics towards their asymptotic profiles, and the overall physical flow organization. In extension of recent studies focusing on the mean flow at moderate and relatively high Re, the latter questions are addressed with respect to three canonical wall-bounded flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Main results reported here are the asymptotic logarithmic law for the mean velocity and corresponding scale-separation laws for bulk flow properties, the Reynolds shear stress, the turbulence production and turbulent viscosity. A scaling analysis indicates that the establishment of a self-similar turbulence state is the condition for the development of a strict logarithmic velocity profile. The resulting overall physical flow structure at extreme Re is discussed.

中文翻译：

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关于湍流壁流的平均流动普遍性。二、渐近流分析

摘要 对极端雷诺数 (Re) 湍流结构的理解是相关的，原因有以下几个：几乎所有湍流理论仅在高 Re 限制下有效，并且大多数具有实际相关性的湍流具有非常高的 Re 特征。关于极端 Re 壁面湍流的具体问题涉及平均速度和湍流统计的渐近定律、它们的普遍性、统计向其渐近剖面的收敛以及整体物理流动组织。在最近关注中等和相对高 Re 下的平均流的研究的扩展中，后一个问题针对三个典型的壁边界流（通道流、管道流和零压力梯度湍流边界层）来解决。这里报告的主要结果是平均速度的渐近对数定律和体积流动特性、雷诺剪切应力、湍流产生和湍流粘度的相应尺度分离定律。标度分析表明，自相似湍流状态的建立是形成严格对数速度剖面的条件。讨论了在极端 Re 下产生的整体物理流结构。