VCG - Double Gyre

Description

2D Double Gyre flow, performs translation of vortices in positive x direction back and forth with distance eps.

Details

The Double Gyre 2D flow consists of two vortices next to on another, moving forward and backward in x-direction with distance specified in eps parameter. The equations are:
$v(x,y,t)= \pi A \begin{pmatrix}-\sin(\pi f(x))\cos(\pi y)\\\cos(\pi f(x))\sin(\pi y) \frac{d f}{dx}\end{pmatrix}$
with
$f(x,t)= \epsilon \sin(\frac{1}{T} t)x^2 + (1-2\epsilon \sin(\frac{1}{T} t))x$ in the domain $[0,2] \times [1,0]$

Model is as described in [Wilde] , [Shadden] .

Input

Output

vtkImageData

Parameters

Name
Description
 Values/Default
A Magnitude of flow velocity. 0.1
T Time range of simulation. 10
eps Distance of vortex translation from starting position. 0.1
OutputSpaceTime Add time dimension to output dimenstions. 0
TimeRange Time range of samples. 0 10
TimeSteps Number of time steps for the samples. 100
Samples Number of samples in each dimension. 100 50
Origin Point of origin for the samples window. 0 0
Scale Scale of sample distance in each dimension. 2 1

Installation Instructions

Authors

Lutz Hofmann

References

S. C. Shadden, F. Lekien, J. E. Marsden:
Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows
Physica D: Nonlinear Phenomena, vol. 212, no. 3, pp. 271 - 304, 2005.

T. Wilde, C. Rossl, H. Theisel:
Recirculation Surfaces for Flow Visualization
IEEE Transactions on Visualization and Computer Graphics, vol. PP, pp. 1-1, 2018.

Acknowledgements