# Polar rotation angle identifies elliptic islands in unsteady dynamical systems

@article{Farazmand2015PolarRA, title={Polar rotation angle identifies elliptic islands in unsteady dynamical systems}, author={Mohammad Farazmand and George Haller}, journal={Physica D: Nonlinear Phenomena}, year={2015}, volume={315}, pages={1-12} }

## 34 Citations

### An autonomous dynamical system captures all LCSs in three-dimensional unsteady flows.

- MathematicsChaos
- 2016

It is observed that, in three dimensions, initial positions of all variational LCSs are invariant manifolds of the same autonomous dynamical system, generated by the intermediate eigenvector field, ξ2(x0), of the Cauchy-Green strain tensor.

### Defining Lagrangian coherent vortices from their trajectories

- Physics, Environmental SciencePhysics of Fluids
- 2020

We study the transport properties of mesoscale eddies (i.e., vortices of 100–200 km in diameter) over a finite time duration. While these oceanic structures are well-known to stir and mix surrounding…

### Extraction of Dynamical Coherent Structures from Time-Varying Data Sets

- Computer Science
- 2016

This research has focused on addressing challenges in systematic and accurate detection of Lagrangian Coherent Structures in reallife flow data by extending LCS methods to scenarios where direct measurement of the velocity field is not feasible.

### Lagrangian coherent structures in flow past a backward-facing step

- PhysicsJournal of Fluid Mechanics
- 2022

Abstract This paper investigates flow past a backward-facing step (BFS) in a duct at Reynolds number $Re = 5080$ based on step height, mean inflow velocity and fluid kinematic viscosity. The flow…

### Global variational approach to elliptic transport barriers in three dimensions.

- MathematicsChaos
- 2016

An approach to identify elliptic transport barriers in three-dimensional, time-aperiodic flows by obtaining explicit expressions for the normals of pointwise (near-) uniformly stretching material surfaces over a finite time interval is introduced.

### Chaos in Hamiltonian systems subjected to parameter drift.

- PhysicsChaos
- 2019

Tori not broken up are shown to be the analogs of coherent vortices in fluid flows of arbitrary time dependence, and the condition for breakup can also be demonstrated by the so-called polar rotation angle method.

### Resonance, symmetry, and bifurcation of periodic orbits in perturbed Rayleigh–Bénard convection

- Physics, MathematicsNonlinearity
- 2023

This paper investigates the global structures of periodic orbits that appear in Rayleigh–Bénard convection, which is modelled by a two-dimensional perturbed Hamiltonian model, by focusing upon…

### Variational Approach to Lagrangian Coherent Structures in Three-Dimensional Unsteady Flows

- Environmental Science
- 2017

Unsteady uid ows, as seen e.g., in the ocean or atmosphere, are mostly turbulent and evolve on numerous time and length scales. Despite these complexities, they produce striking tracer patterns that…

### Defining coherent vortices objectively from the vorticity

- Physics, Environmental ScienceJournal of Fluid Mechanics
- 2016

Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We…

### Erratum:“Quasi-objective coherent structure diagnostics from single trajectories” [Chaos 31, 043131 (2021)]

- PhysicsChaos: An Interdisciplinary Journal of Nonlinear Science
- 2022

We derive measures of local material stretching and rotation that are computable from individual trajectories without reliance on other trajectories or on an underlying velocity field. Both measures…

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Rotationally coherent Lagrangian vortices are formed by tubes of deforming fluid elements that complete equal bulk material rotation relative to the mean rotation of the deforming fluid volume. We…

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