Addressing the threats of climate change, pollution, and overfishing to marine ecosystems necessitates a deeper understanding of coastal and oceanic fluid dynamics. Within this context, Lagrangian Coherent Structures (LCS) emerge as essential tools for elucidating the complexities of marine fluid dynamics. Methods used to detect LCS include geometric, probabilistic, cluster-based and braid-based approaches. Advancements have been made to employ Finite-time Lyapunov Exponents (FTLE) to detect LCS due to its high efficacy, reliability and simplicity. It has been proven that the FTLE approach has provided invaluable insights into complex oceanic phenomena like shear, confluence, eddy formations, and oceanic fronts, which also enhanced the understanding of tidal-/wind-driven processes. Additionally, FTLE-based LCS were crucial in identifying barriers to contaminant dispersion and assessing pollutant distribution, aiding environmental protection and marine pollution management. FTLE-based LCS has also contributed significantly to understanding ecological interactions and biodiversity in response to environmental issues. This review identifies pressing challenges and future directions of FTLE-based LCS. Among these are the influences of external factors such as river discharges, ice formations, and human activities on ocean currents, which complicate the analysis of ocean fluid dynamics. While 2D FTLE methods have proven effective, their limitations in capturing the full scope of oceanic phenomena, especially in 3D environments, are evident. The advent of 3D LCS analysis has marked progress, yet computational demands and data quality requirements pose significant hurdles. Moreover, LCS extracted from FTLE fields involves establishing an empirical threshold that introduces considerable variability due to human judgement. Future efforts should focus on enhancing computational techniques for 3D analyses, integrating FTLE and LCS into broader environmental models, and leveraging machine learning to standardize LCS detection.

中文翻译：

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有限时间李亚普诺夫指数在检测沿海海洋过程拉格朗日相干结构中的应用：综述


应对气候变化、污染和过度捕捞对海洋生态系统的威胁需要更深入地了解沿海和海洋流体动力学。在此背景下，拉格朗日相干结构（LCS）成为阐明海洋流体动力学复杂性的重要工具。用于检测 LCS 的方法包括几何方法、概率方法、基于簇的方法和基于辫子的方法。由于其高效性、可靠性和简单性，有限时间李雅普诺夫指数 (FTLE) 检测 LCS 已取得进展。事实证明，FTLE 方法为复杂的海洋现象（如剪切、汇合、涡流形成和海洋锋面）提供了宝贵的见解，这也增强了对潮汐/风驱动过程的理解。此外，基于 FTLE 的 LCS 对于识别污染物扩散障碍和评估污染物分布、帮助环境保护和海洋污染管理至关重要。基于 FTLE 的 LCS 还为了解生态相互作用和生物多样性以应对环境问题做出了重大贡献。本次审查确定了基于 FTLE 的濒海战斗舰面临的紧迫挑战和未来方向。其中包括河流流量、冰层形成和人类活动等外部因素对洋流的影响，这使得海洋流体动力学分析变得复杂。虽然 2D FTLE 方法已被证明是有效的，但它们在捕获全部海洋现象（尤其是在 3D 环境中）方面的局限性是显而易见的。 3D LCS 分析的出现取得了显着的进步，但计算需求和数据质量要求构成了重大障碍。 此外，从 FTLE 场中提取的 LCS 涉及建立一个经验阈值，该阈值会因人类判断而引入相当大的可变性。未来的努力应集中于增强 3D 分析的计算技术，将 FTLE 和 LCS 集成到更广泛的环境模型中，并利用机器学习来标准化 LCS 检测。