In the late 19th century, Osborne Reynolds published two papers whose impact on atmospheric turbulence studies can hardly be overstated. The first, Reynolds (1883) established both his eponymous, dimensionless number and his reputation as the father of turbulence science, which is beyond doubt. However, his second famous paper (Reynolds, 1895) sowed seeds of confusion regarding the mathematical separation of average (mean) and fluctuating (turbulent) components of a fluid flow. Here, we revisit both the prehistory and after-effects of Reynolds's second famous article, which seems to have been published largely thanks to his already entrenched reputation.We show that successions of authors have misrepresented Reynolds's innovations – now known as Reynolds averaging and decomposition (RAAD) –, putting his name to methodologies that he never intended. We attribute this, in part, to Reynolds's predilection for long, inscrutable sentences, as well as his self-contradiction regarding the methodology for averaging the normal stress (or pressure). We examine two additional issues that are intimately related to using RAAD to define turbulent fluxes, namely its application to intensive versus extensive variables and the appearance of “Leonard terms” in the averaged equation of motion, neither of which is completely resolved. Throughout the manuscript, we identify a set of unanswered questions concerning RAAD and conclude that a complete mathematical description of turbulence is unlikely to emerge without addressing these issues, including the original inconsistency that was introduced by Osborne Reynolds himself.

中文翻译：

---

探索有关雷诺平均和分解含义的未解决的问题：综述


19 世纪末，奥斯本·雷诺兹 （Osborne Reynolds） 发表了两篇论文，对大气湍流研究的影响怎么强调都不为过。第一个是 Reynolds （1883） 确立了他的同名无量纲数和他作为湍流科学之父的声誉，这是毋庸置疑的。然而，他的第二篇著名论文（Reynolds，1895 年）在流体流动的平均（平均值）和波动（湍流）分量的数学分离方面播下了混淆的种子。在这里，我们回顾了雷诺兹第二篇著名文章的史前史和后遗症，这篇文章的发表似乎在很大程度上要归功于他已经根深蒂固的声誉。我们表明，连续的作者歪曲了雷诺兹的创新——现在被称为雷诺平均和分解 （RAAD）——将他的名字放在了他从未想过的方法上。我们将其部分归因于雷诺兹偏爱长而高深莫测的句子，以及他对平均正常压力（或压力）的方法的自相矛盾。我们研究了与使用 RAAD 定义湍流通量密切相关的两个其他问题，即它在密集变量与广泛变量中的应用，以及平均运动方程中“伦纳德项”的出现，这两个问题都没有完全解决。在整个手稿中，我们确定了一组关于 RAAD 的未解之谜，并得出结论，如果不解决这些问题，包括奥斯本·雷诺兹 （Osborne Reynolds） 本人提出的最初不一致，就不太可能出现对湍流的完整数学描述。