Time-Dependent 2-D Vector Field Topology: An Approach Inspired by Lagrangian Coherent Structures

This paper presents an approach to a time-dependent variant of the concept of vector field topology for 2-D vector fields. Vector field topology is defined for steady vector fields and aims at discriminating the domain of a vector field into regions of qualitatively different behaviour. The presented approach represents a generalization for saddle-type critical points and their separatrices to unsteady vector fields based on generalized streak lines, with the classical vector field topology as its special case for steady vector fields. The concept is closely related to that of Lagrangian coherent structures obtained as ridges in the finite-time Lyapunov exponent field. The proposed approach is evaluated on both 2-D time-dependent synthetic and vector fields from computational fluid dynamics

Oceanic three-dimensional Lagrangian Coherent Structures: A study of a mesoscale eddy in the Benguela ocean region

We study three dimensional oceanic Lagrangian Coherent Structures (LCSs) in the Benguela region, as obtained from an output of the ROMS model. To do that we first compute Finite-Size Lyapunov exponent (FSLE) fields in the region volume, characterizing mesoscale stirring and mixing. Average FSLE values show a general decreasing trend with depth, but there is a local maximum at about 100 m depth. LCSs are extracted as ridges of the calculated FSLE fields. They present a "curtain-like" geometry in which the strongest attracting and repelling structures appear as quasivertical surfaces. LCSs around a particular cyclonic eddy, pinched off from the upwelling front are also calculated. The LCSs are confirmed to provide pathways and barriers to transport in and out of the eddy

On the role of domain-specific knowledge in the visualization of technical flows

In this paper, we present an overview of a number of existing flow visualization methods, developed by the authors in the recent past, that are specifically aimed at integrating and leveraging domain-specific knowledge into the visualization process. These methods transcend the traditional divide between interactive exploration and featurebased schemes and allow a visualization user to benefit from the abstraction properties of feature extraction and topological methods while retaining intuitive and interactive control over the visual analysis process, as we demonstrate on a number of examples

Transport in Transitory Dynamical Systems

We introduce the concept of a "transitory" dynamical system---one whose time-dependence is confined to a compact interval---and show how to quantify transport between two-dimensional Lagrangian coherent structures for the Hamiltonian case. This requires knowing only the "action" of relevant heteroclinic orbits at the intersection of invariant manifolds of "forward" and "backward" hyperbolic orbits. These manifolds can be easily computed by leveraging the autonomous nature of the vector fields on either side of the time-dependent transition. As illustrative examples we consider a two-dimensional fluid flow in a rotating double-gyre configuration and a simple one-and-a-half degree of freedom model of a resonant particle accelerator. We compare our results to those obtained using finite-time Lyapunov exponents and to adiabatic theory, discussing the benefits and limitations of each method.Comment: Updated and corrected version. LaTeX, 29 pages, 21 figure