Identification of Hyperbolic Lagrangian Coherent Structures in Three-Dimensional Time-Varying Flow

Lagrangian coherent structures (LCSs) are dynamic surfaces that shape the flow patterns in complex transport systems. Accurate identification of LCSs has applications in Lagrangian particle transport, including dissemination of oil in water following major oil spills and airborne ash after volcanic eruptions. While methods exist for identifying LCSs by use of their variational theory in two-dimensional systems, limited effort has previously been given to extending these methods to three dimensions. Where some systems may reasonably be approximated as two-dimensional, LCSs in other firmly three-dimensional systems have commonly been computed by combining two-dimensional cross sections.

Aiming to develop a dedicated method for computing three-dimensional hyperbolic LCSs, this study combines existing LCS theory with adaptations of recognized methods for computing three-dimensional manifolds, in particular the method of geodesic level sets. We outline the theory and numerical methods, and present the results of applying the complete method to a well-known test case, the (steady and unsteady) ABC flow. Furthermore, we apply the method to three-dimensional ocean current data from a high-resolution hydrodynamic model, and identify a strongly repelling LCS using an integration interval of 12 hours.