Lagrangian Coherent Structures

Typical fluid particle trajectories are sensitive to changes in their initial conditions. This makes the assessment of flow models and observations from individual tracer samples unreliable. Behind complex and sensitive tracer patterns, however, there exists a robust skeleton of material surfaces, Lagrangian coherent structures (LCSs), shaping those patterns. Free from the uncertainties of single trajectories, LCSs frame, quantify, and even forecast key aspects of material transport. Several diagnostic quantities have been proposed to visualize LCSs. More recent mathematical approaches identify LCSs precisely through their impact on fluid deformation. This review focuses on the latter developments, illustrating their applications to geophysical fluid dynamics.