发表机构
IMT Atlantique; Inria; CNRS; ENS de Lyon; CEA（大西洋高等矿业电信学院; 法国国家信息与自动化研究所; 法国国家科学研究中心; 里昂师范学院; 法国原子能和替代能源委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究利用实验数据，采用洛伦兹的类似物方法，识别出湍流误差增长的三种机制，揭示了相关指数对初始误差的依赖关系，验证了洛伦兹的直觉并为极端事件预测提供了新见解。
AI 中文摘要
本研究利用实验数据，重新审视洛伦兹（Lorenz）提出的类似物这一开创性概念，以探究充分发展湍流中的误差增长与可预测性。将该方法应用于一维湍流速度时间序列，成功识别出洛伦兹所直觉提出、后经湍流理论形式化的三种误差增长机制：混沌指数机制、自发随机性的代数机制及饱和机制。分析表明，李雅普诺夫指数与代数机制的指数依赖于初始误差，将此依赖解释为湍流间歇性引发的统计偏差——当考虑更大初始误差时，会优先采样到由更低李雅普诺夫指数、更奇异速度增量表征的稀有事件。这些发现不仅验证了洛伦兹的定性直觉，还为湍流的可预测性提供了新的定量见解，为极端事件预测的潜在应用铺平了道路。
英文摘要
In this study, we revisit Lorenz's pioneering concept of analogues to investigate error growth and predictability in fully developed turbulence using experimental data. By applying the method to a 1D turbulent velocity time series, we successfully identify the three error growth regimes intuited by Lorenz and later formalized by turbulence theory: the chaotic exponential regime, the algebraic regime of spontaneous stochasticity, and the saturation regime. Our analysis reveals that the Lyapunov exponent and the exponent of the algebraic regime depend on the initial error. We interpret this dependence as a statistical bias induced by the intermittency of turbulence, where rare events, characterized by lower Lyapunov exponents and more singular velocity increments, are preferentially sampled when considering larger initial errors. These findings not only validate Lorenz's qualitative intuition but also provide new quantitative insights into the predictability of turbulent flows, paving the way for potential applications in the prediction of extreme events.
