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One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time-and-space semidistance that comes from the “best” approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases. [ABSTRACT FROM AUTHOR]

Abstract: The ocean is a very complex medium with scales of motion that range from thousands of kilometers to the dissipation scales. Transport by ocean currents plays an important role in many practical applications ranging from climatic problems to coastal management and accident mitigation at sea. Understanding transport is challenging because of the chaotic nature of particle motion. In the last decade, new methods have been put forth to improve our understanding of transport. Powerful tools are provided by dynamical system theory, that allow the identification of the barriers to transport and their time variability for a given flow. A shortcoming of this approach, though, is that it is based on the assumption that the velocity field is known with good accuracy, which is not always the case in practical applications. Improving model performance in terms of transport can be addressed using another important methodology that has been recently developed, namely the assimilation of Lagrangian data provided by floating buoys. The two methodologies are technically different but in many ways complementary. In this paper, we review examples of applications of both methodologies performed by the authors in the last few years, considering flows at different scales and in various ocean basins. The results are among the very first examples of applications of the methodologies to the real ocean including testing with Lagrangian in-situ data. The results are discussed in the general framework of the extended fields related to these methodologies, pointing out to open questions and potential for improvements, with an outlook toward future strategies. [Copyright &y& Elsevier]

Abstract: We present a suite of algorithms for migrating Lagrangian data between processors in a parallel environment when the underlying mesh is Eulerian. The collection of algorithms applies to both uniform and adaptive meshes. The algorithms are implemented in, and distributed with, FLASH, a publicly available multiphysics simulation code. Migrating Lagrangian data on an Eulerian mesh is non-trivial because the Eulerian grid points are spatially fixed whereas Lagrangian entities move with the flow of a simulation. Thus, the movement of Lagrangian data cannot use the data migration methods associated with the Eulerian mesh. Additionally, when the mesh is adaptive, as the simulation progresses the grid resolution changes. The resulting regridding process can cause complex Lagrangian data migration. The algorithms presented in this paper describe Lagrangian data movement on a static uniform mesh and on an adaptive octree based block-structured mesh. Some of the algorithms are general enough to be applicable to any block structured mesh, while some others exploit the meta-data and structure of PARAMESH, the adaptive mesh refinement (AMR) package used in FLASH. We also present an analysis of the algorithms’ comparative performances in different parallel environments, and different flow characteristics. [Copyright &y& Elsevier]

Lagrangian data of surfzone flows are scarce, but important for understanding the spatial variability of currents. Surfzone drifters capable of collecting high frequency, accurate, Lagrangian data in the surfzone have been developed. The main issues of a robust design capable of autonomous positioning fixing, the dynamic response of the drifters, position fixing accuracy and field validation are addressed. A simple, low-cost drifter design using non-differential Global Positioning System (GPS) position fixing is described. A drogue consisting of a series of small parachutes prevents the drifter surfing in breaking waves. The methodology and results of simulations of drifter response in idealised surfzone waves are presented and predict that the drifter will perform well in low to medium energy surfzones. An analysis of positioning errors shows that only surfzone motions with frequencies of less than 0.05 Hz can be reliably resolved without differential correction. A field validation of the drifters shows that although there is significant scatter in the data, the best-fit correspondence of the drifter velocity and depth-averaged Acoustic Doppler Current Profiler (ADCP) measurements is good. [Copyright &y& Elsevier]

Abstract: The reconstruction of currents at 50 m depth was performed in the Gulf of Lions, merging Lagrangian data with outputs from a numerical ocean model. The Lagrangian data set consists of trajectories obtained from 12 satellite-tracked drifters released in the Northern Current in June 2005. The low-pass filtered trajectories revealed the well-known mean patterns of along-slope circulation and sampled its mesoscale activity, showing meandering pathways over the slope and closed pathways trapped over the shelf. They were used to reorganise the model eddy activity by refining the location and shape of meanders and eddies. The impacts of the reconstruction procedure were assessed by comparing the simulated and reconstructed fields with simultaneous SST images. Finally, the reconstructed fields were used to study some of the observed mesoscale structures. They provide a realistic scenario for diagnostics of the shelf-slope transports in the Gulf of Lions. [Copyright &y& Elsevier]