Chapter 4 Vortex detection - Computer Graphics and Visualization

4.6. Conclusions
which are not perfectly circular. Another important advantage is that it allows for
quantification of vortices by calculating numerical attributes. The third major advantage
of this method is that it also finds weak vortices, characterized by slow rotational
movement. This will be shown in more detail in another application in Section 6.2.5.
4.6 Conclusions
We have shown examples of physical criteria and geometric criteria for vortex detection.
Physical, point-based criteria are of limited use, because there does not seem to
exist a generally accepted criterion, which works in all cases. An important drawback
of physical criteria is that they usually do not detect weak vortices, because they often
involve the velocity magnitude or another strength factor, directly or indirectly.
In principle, geometric, region-based criteria are better, because they correspond to
the intuitive visual notion of a vortex, and because they are based on the properties
of a whole region, such as a streamline or a number of streamlines. The curvature
centre method performs well in finding (nearly) perfectly circular vortices, but it does
not find elliptical and weak vortices. Possible enhancements to the curvature centre
method have been investigated, but did not give a satisfactory result either.
The winding-angle method is much better, because it can detect not only noncircular
but also weak vortices. Another important advantage is that it allows for
quantification of vortices.
Chapter 6 will show more comprehensive examples of data sets to which these
vortex detection criteria are applied.
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