Chapter 4 Vortex detection - Computer Graphics and Visualization

¯ vortex rotation direction: ×Ò «Û
¯ vortex angular velocity: ¡Ø
4.5. The winding-angle method
È
Ð «ÛÐ
Visualization of the vortices can be accomplished by mapping their attributes to icons:
the first three attributes are mapped to an ellipse. The angular velocity is visualized
by adding wheel spokes to the ellipse, the number of which is made proportional to
the angular velocity: fast rotation is suggested by many spokes, slow rotation by few.
Finally, the rotation direction of a vortex is visualized by arrow heads.
4.5.2 Example
To test this method, we use the same flow past the tapered cylinder as in Section 4.1.
First, we apply the winding-angle method to select streamlines from six slices in various
z-planes, to show varying patterns. The selection criteria are: «Û and
ÑÜ× .
Next, we apply clustering with maximum cluster radius 0.5, and quantification,
which results in the numeric attributes listed in Table 4.2. This table reveals that for Þ
, there is only one counterclockwise vortex, for Þ , there are two vortices,
one clockwise and one counterclockwise, and for Þ , the counterclockwise vortex
has disappeared, leaving only a large clockwise vortex.
z-plane #vortices ÑÜ Ï ÑÜ Ï
16 1 - 0.5305
17 1 - 0.5832
18 1 0.6216 0.2076
19 2 0.8446 0.4968
20 2 1.1138 0.6117
21 1 - 0.9370
Table 4.2: Statistics of the vortices in the flow past a tapered cylinder.
Figure 4.15 shows the visualization of these vortices. Grey streamlines show the
global flow patterns, with the flow going from left to right past the cylinder, which is
drawn as a semi-circle on the left. Selected streamlines are drawn in black. The ellipses
approximate the shape and size of the vortices, with arrows indicating the rotation
direction, and the number of spokes indicating the rotation speed (vortex strength):
more spokes indicate faster rotation.
The middle image on the back cover shows a slightly different visualization of
Figure 4.15e Þ , with different ellipse icons. These do not have the varying
number of spokes, but the colour indicates the rotation direction: the red ellipse shows
counterclockwise rotation, the green one clockwise rotation.
This example shows that this method produces better results than the physical criteria
or the curvature centre method. One advantage is that it finds rotating structures
67