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.
