Lagrangian Coherent Structures ?

Have you ever noticed swirling, billowing, or circular patterns in the ocean, rivers, or sky, like these shown images below (Figure 1) ?

At first glance, these features may seem chaotic, ephemeral and unpredictable and they are indeed difficult to study with traditional modelling and observation approaches. The main reason is that trajectories of fluid parcels can be very sensitive to their initial conditions (e.g. starting on either side of an eddy), and studying individual tracers may provide unreliable estimates of the overall transport.

However, behind the complexity of individual tracer patterns, there are robust skeletons of fluid flows, termed “Lagrangian Coherent Structures" (LCS) which shape these patterns. The LCS are free from the uncertainties of single trajectories and provide a valuable framework to identify, quantify, and forecast the key transport features, in the ocean, atmosphere or any fluid. More specifically, LCS identifies regions within a fluid that exhibit the strongest attraction, repulsion, or shearing behavior over a given location and  time interval. These structures act as invisible barriers and fronts, organizing the flow into distinct regions and influencing how material, such as pollutants (plastic, oil, debris), marine organisms, or geophysical quantities (heat, salt, nutrient) move through the ocean.

LCS provides a powerful new way of looking at ocean circulation, transport and connectivity. A useful analogy is they inform on the “weather” of the oceans; identifying independent transport regions, locating dynamical fronts between them, and how they interact.