Topology of a Velocity Field

Copyright (c) 1994 Academic Press from Scientific Visualization - Advances and Challenges. Chapter 26: Visualization of vector and tensor data sets, pp. 419-433.

Lambertus Hesselink and Thierry Delmarcelle visualize velocity fields by extracting its topological sceleton. The above image shows how a flow near the body of a hemisphere cylinder is visualized by extracting the topology of the Jacobian of the velocity field: critical points (foci, saddles, attracting and repelling nodes) are located then and connected by integrating streamlines along the saddle points.
In image 7 we show how a similar method is can be applied to a general tensor field.