AI 中文总结
本文针对流体力学中自相似性识别问题，基于已有数据驱动框架开发算法，可系统识别多尺度自相似性，应用于多个典型流体力学问题，成功提取相似性表达式并发现相关定律修正，为研究流体流动特性提供新途径。
AI 中文摘要
流体力学中的核心问题是自相似性识别，它揭示了流动的潜在标度行为。Bempedelis等人提出的数据驱动框架能从数据中提取单尺度自相似性。在此基础上，本文开发了一种系统识别多尺度自相似性的算法。该算法先应用于两个典型流体力学问题，成功识别出内、外自相似性并恢复相应相似表达式，还发现了对两个定律的修正。最后应用于早期均匀衰减湍流，识别出不同的外相似表达式。
英文摘要
A central problem in fluid mechanics is the identification of self-similarity, which reveals the underlying scaling behaviour of a flow. Recently, a data-driven framework proposed by Bempedelis et al. (2025 J. Fluid Mech., vol. 1020, A11) has enabled the extraction of single-scale self-similarity from data, without prior knowledge of the governing equations. However, many physical systems are inherently multiscale and therefore require more general approaches. Building on this foundation, we develop an algorithm for the systematic identification of multiscale self-similarity. The algorithm is first applied to two canonical fluid-mechanical problems: turbulent channel flow and late-stage homogeneous decaying turbulence characterised by classical dissipation laws. In both cases, the algorithm successfully identifies inner and outer self-similarity from numerical data and recovers the corresponding similarity expressions. In the intermediate region of both problems, the algorithm identifies similarity expressions that are independent of both the inner and outer scales, providing a novel data-driven route to recovering the corresponding scaling laws: the logarithmic law in turbulent channel flow and the -5/3 law in late-stage homogeneous decaying turbulence. Moreover, the algorithm uncovers corrections to both laws: one linked to the power-law scaling proposed by Barenblatt (1993 J. Fluid Mech., vol. 248, 513--520), and the other yielding an improved approximation of the energy spectrum. The algorithm is then applied to early-stage homogeneous decaying turbulence, characterised by the nonclassical dissipation law. It identifies the same inner similarity as in the late stage, but different outer similarity expressions.
