Turbulence is often studied by tracking its spatiotemporal evolution and analyzing the dynamics of its different scales. The dual to this perspective is that of an observer who starts from measurements, or observations, of turbulence and attempts to identify their back-in-time origin, which is the foundation of data assimilation. This back-in-time search must contend with the action of chaos, which obfuscates the interpretation of the observations. When the available measurements satisfy a critical resolution threshold, the influence of chaos can be entirely mitigated and turbulence can be synchronized to the exact state–space trajectory that generated the observations. The critical threshold offers a new interpretation of the Taylor microscale, one that underscores its causal influence. Below the critical threshold, the origin of measurements becomes less definitive in regions where the flow is inconsequential to the observations. In contrast, flow events that influence the measurements, or are within their domain of dependence, are accurately captured. The implications for our understanding of wall turbulence are explored, starting with the highest density of measurements that entirely tame chaos and proceeding all the way to an isolated measurement of wall stress. The article concludes with a discussion of future opportunities and a call to action.

中文翻译：

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观察者视角下的湍流


湍流通常通过追踪其时空演变并分析其不同尺度的动力学来研究。这种视角的双重性是观察者从湍流的测量或观察开始，并试图确定它们的回溯起源，这是数据同化的基础。这种时间倒流的搜索必须与混沌的作用相抗衡，混沌混沌会混淆对观察结果的解释。当可用测量值满足临界分辨率阈值时，混沌的影响可以完全减轻，并且湍流可以与产生观测值的确切状态-空间轨迹同步。临界阈值为泰勒微观尺度提供了新的解释，强调了其因果影响。低于临界阈值时，在流量对观测无关紧要的区域中，测量的来源变得不那么确定。相比之下，影响测量或在其依赖域内的流事件被准确捕获。探讨了对我们理解壁湍流的影响，从完全驯服混沌的最高测量密度开始，一直到壁应力的孤立测量。本文最后讨论了未来的机会并呼吁采取行动。