Quasi-Objective Eddy Visualization from Sparse Drifter Data

We employ a recently developed single-trajectory Lagrangian diagnostic tool, the trajectory rotation average $(\mathrm{\overline{TRA}})$, to visualize oceanic vortices (or eddies) from sparse drifter data. We apply the $\mathrm{\overline{TRA}}$ to two drifter data sets that cover various oceanographic scales: the Grand Lagrangian Deployment (GLAD) and the Global Drifter Program (GDP). Based on the $\mathrm{\overline{TRA}}$, we develop a general algorithm that extracts approximate eddy boundaries. We find that the $\mathrm{\overline{TRA}}$ outperforms other available single-trajectory-based eddy detection methodologies on sparse drifter data and identifies eddies on scales that are unresolved by satellite-altimetry

Relative Fluid Stretching and Rotation for Sparse Trajectory Observations

As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists working with Lagrangian trajectory data via passive tracers in unsteady flows (e.g. Lagrangian particle tracking or ocean buoys), obtaining material measures of fluid rotation or stretching is currently only possible for trajectory concentrations that are often out-of-reach. To facilitate frame-indifferent investigations in unsteady and sparsely sampled flows, we present a novel approach to quantify fluid stretching and rotation via relative Lagrangian velocities. This technique provides a formal objective extension of quasi-objective metrics to unsteady flows by accounting for mean flow behavior. For extremely sparse experimental data, fluid structures may be significantly undersampled, and the mean flow behavior becomes difficult to quantify. We provide a means to maintain the accuracy of our novel sparse flow diagnostics in extremely sparse sampling scenarios, such as ocean buoy data and Lagrangian particle tracking. We use data from multiple numerical and experimental flows to show that our methods can identify structures beyond existing limits of sparse, frame-indifferent diagnostics, and exhibit improved interpretability over common frame-dependent diagnostics