When discussing research in physics and in science more generally, it is common to ascribe equal importance to the three components of the scientific trinity: theoretical, experimental, and computational studies. This review will explore the future of modern turbulence theory by tracing its history, which began in earnest with Kolmogorov’s 1941 analysis of turbulence cascade and inertial range (Kolmogorov, 1941a, 1941d). The 80th Anniversary of Kolmogorov’s landmark study is a welcome opportunity to survey the achievements and evaluate the future of the theoretical approach of turbulence research. Over the years, turbulence theories have been critically important in laying the foundation of our understanding of the nature of turbulent flows. In particular, the Direct Interaction Approximation (DIA) (Kraichnan, (1959a) and its subsequent development, known as the statistical closure approach, can be identified as perhaps the most profound single advancement. The remarkable success of the statistical closure has furnished a platform to study such essential concepts as the energy transfer process and interacting scales, and the roles of the straining and sweeping motions. More recently, the quasi-Lagrangian formulation of V. L’vov & I. Procaccia and Kraichnan’s solvable passive scalar model provided powerful ways to explore another fundamental aspect of turbulent flows, the phenomena of intermittency, and the associated anomalous scaling exponents. In the meantime, the theory of fluid equilibria has been developed to describe the large-scale structures that can emerge from turbulent cascades of two-dimensional and geophysical flows at a later time. And yet, despite all these successes, analytical treatments suffer from mathematical complexities. As a result, the utility of theoretical approaches has been limited to relatively idealized flows. On the other hand, in recent decades, computational abilities and experimental facilities have reached an unprecedented scale. Looking beyond the horizon, the imminent deployment of exascale supercomputers will generate complete datasets of the entire flow field of key benchmark flows, allowing researchers to extract additional measurements concerning fully developed, complex turbulent flow fields far beyond those available from the statistical closure theories. Some other developments that could potentially influence the future course of turbulence theories include the advancement of machine learning, artificial intelligence, and data science; likely disruptions arising from the advent of quantum computation; and the increasingly prominent role of turbulence research in providing more accurate climate scientific data. Turbulence theorists can leverage these developments by asking the right questions and developing advanced, sophisticated frameworks that will be able to predict and correlate vast amounts of data from the other two components of the trinity.

在更广泛地讨论物理学和科学研究时，通常认为科学三位一体的三个组成部分同等重要：理论研究、实验研究和计算研究。这篇综述将通过追溯现代湍流理论的历史来探索它的未来，它始于 Kolmogorov 1941 年对湍流级联和惯性范围的分析（Kolmogorov，1941a，1941d）。Kolmogorov 具有里程碑意义的研究 80 周年是一个很好的机会来调查湍流研究的理论方法的成就和评估其未来。多年来，湍流理论在为我们理解湍流的性质奠定基础方面发挥了至关重要的作用。特别是直接交互逼近 (DIA) (Kraichnan, （1959a）及其随后的发展，被称为统计闭包方法，可能被认为是最深刻的单一进步。统计闭包的显着成功为研究诸如能量转移过程和相互作用尺度以及应变和扫掠运动的作用等基本概念提供了一个平台。最近，V. L'vov 和 I. Procaccia 的准拉格朗日公式以及 Kraichnan 的可解被动标量模型提供了强大的方法来探索湍流的另一个基本方面、间歇现象和相关的异常标度指数。与此同时，流体平衡理论已经发展起来，以描述后来可能从二维和地球物理流动的湍流级联中出现的大规模结构。然而，尽管取得了所有这些成功，但分析处理仍存在数学复杂性。因此，理论方法的效用仅限于相对理想化的流动。另一方面，近几十年来，计算能力和实验设施达到了前所未有的规模。展望未来，即将部署的百亿亿级超级计算机将生成关键基准流的整个流场的完整数据集，使研究人员能够提取有关完全发展的复杂湍流流场的额外测量值，远远超出统计闭合理论所能提供的测量值。可能影响湍流理论未来进程的其他一些发展包括机器学习、人工智能和数据科学的进步；量子计算的出现可能引起的中断；湍流研究在提供更准确的气候科学数据方面的作用日益突出。湍流理论家可以通过提出正确的问题和开发先进、复杂的框架来利用这些发展，这些框架将能够预测和关联来自三位一体的其他两个组成部分的大量数据。