This project is part of the DRI on Scalable Lateral Mixing and Coherent Turbulence that aims to characterize lateral mixing in the ocean on scales of 10m-10 km, the submesoscales. Lateral mixing at the submesoscales is not accounted for in present-day ocean models. This deficiency is a potential source of error in the numerical prediction of the distribution of temperature, salt, nutrients, phy...

Lagrangian coherent structures (LCSs) have become a widespread and powerful method to describe dynamic motion patterns in time-dependent flow fields. The standard way to extract LCS is to compute height ridges in the finite-time Lyapunov exponent field. In this work, we present an alternative method to approximate Lagrangian features for 2D unsteady flow fields that achieve subgrid accuracy wit...

This paper presents a collaborative control strategy designed to enable a team of robots to track attracting Lagrangian coherent structures (LCS) and unstable manifolds in two-dimensional flows. Tracking LCS in dynamical systems is important for many applications such as planning energy optimal paths in the ocean and predicting various physical and biological processes in the ocean. Similar to ...

A numerical investigation is presented into the relation between finite sized, inertial particle transport and entrainment in the vortex-dominated wake of a square cylinder placed in a channel at two blockage ratios and Lagrangian Coherent Structures (LCS) identified with recent Lagrangian visualization techniques. The square cylinder flow is computed with the incompressible, viscous flow solve...

The objective of this paper is to understand transport behavior in uncertain time-varying flow fields by redefining the finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structure (LCS) as stochastic counterparts of their traditional deterministic definitions. Three new concepts are introduced: the distribution of the FTLE (D-FTLE), the FTLE of distributions (FTLE-D), and uncertain L...

In this supplementary material, we present some additional details and results for our paper. The sampling procedure used in our graphical model is in Section 2. The entire set of 46 orientation fields used as the “library” FOFs are presented in Section 3. Comparison of our segmentation results to various other methods is presented in Section 4. In Section 5, we compare our model to other model...

Crowd tracking generates trajectories of a set of particles for further analysis of crowd motion patterns. In this paper, we try to answer the following questions: what are the particles appropriate for crowd tracking and how to track them robustly through crowd. Different than existing approaches of computing optical flows, tracking keypoints or pedestrians, we propose to discover distinctive ...

Video inpainting consists in recovering the missing or corrupted parts of an image sequence so that the reconstructed sequence looks natural. For each frame, the reconstruction has to be spatially coherent with the rest of the image and temporally with respect to the reconstructions of adjacent frames. Most of existing methods only focus on inpainting foreground objects moving with a periodic m...

This project is part of the DRI on Scalable Lateral Mixing and Coherent Turbulence that aims to characterize lateral mixing in the ocean on scales of 10m-10 km, the submesoscales. Lateral mixing at the submesoscales is not accounted for in present-day ocean models. This deficiency is a potential source of error in the numerical prediction of the distribution of temperature, salt, nutrients, phy...

Lagrangian coherent structures (LCSs) are exceptional material surfaces that act as cores of observed tracer patterns in fluid flows (see [1,2] for reviews). For oceanic flows, the tracers of interest include salinity, temperature, contaminants, nutrients and plankton—quantities that play an important role in the ecosystem and even in the climate. Fluxes of these quantities are typically domina...