Dynamical systems theory approach in oceanography: a review on achievements, limitations, verification and validation of Lagrangian methods - Prants, S. V. (Frontiers in Marine Science, 2025)
The Lagrangian approach (LA) in ocean modelling relies on a dense set of trajectories of virtual particles that can be computed using velocity fields and on a subsequent analysis of entangled trajectories of particles. The modern LA explores dynamical systems theory (DST) methods to detect locations of geometric structures hidden in chaotic fluid flows and organizing transport, stirring and mixing in the ocean. The accuracy of calculations critically depends on the quality of the velocity fields obtained using the altimetry data or outputs of the numerical circulation models. The extensive material on Lagrangian studies in oceanography is combined into a comprehensive review emphasizing achievements and limitations of this approach. The fields of various indicators of water motion along particle’s trajectories are represented on geographic maps (Lagrangian maps) with the superimposed locations of elliptic and hyperbolic stagnation points allowing us to detect coherent structures, transport barriers, eddies and fronts. The sensitivity of these structures to imperfections of velocity fields is discussed. Special attention is paid to verification of simulation results, using satellite remote-sensing and float’s data, ship-board measurements and field experiments with drifters. The LA and DST have proven to be successful in the practical issues such as dispersal of anthropogenic and natural pollutants, transport of larvae and searching for potential feeding and fishing grounds. The flux across the Lagrangian structures is usually negligible, and therefore these structures act as transport barriers preventing spread of spilled oil, debris or harmful algae across them. Due to inherent properties of these structures, there is a possibility of the short-term forecast of the locations of well-defined transport barriers contributing to the mitigation of ocean pollution.