VCG - Double Gyre 3D

Description

3D Double Gyre flow, performs translation of vortices in positive x direction back and forth with distance eps. Essentially 2D Double Gyre extruded into the z-axis.

Details

The Double Gyre 3D flow consists of two vortices next to on another, moving forward and backward in x-direction with distance specified in eps parameter. The equations for this flow are as follows:
$v(x,y,t)= \pi A \begin{pmatrix}-\sin(\pi f(x))\cos(\pi y)\\\cos(\pi f(x))\sin(\pi y) \frac{d f}{dx}\\ \frac{1}{5} z (1-z)(z -\epsilon \sin (4\pi\frac{t}{T})-\frac{1}{2})\end{pmatrix}$
with
$f(x,t)= \epsilon \sin(\frac{1}{T} t)x^2 + (1-2\epsilon \sin(\frac{1}{T} t))x$ in the domain $[0,2] \times [1,0] \times [1,0]$

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. 0.25
OutputSpaceTime Add time dimension to output dimenstions. 0
TimeRange Time range of samples. 0.0 10.0
TimeSteps Number of time steps for the samples. 100
Samples Number of samples in each dimension. 100 50 50
Origin Point of origin for the samples window. 0.0 0.0 0.0
Scale Scale of sample distance in each dimension. 2.0 1.0 1.0

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