On the velocity gradient tensor and fluid feature extraction

A 3-D Computational Fluid Dynamics flow field may contain many topological features such as vortex cores, separation surfaces, shock surfaces, and recirculation bubbles. We describe several techniques that identify these global features using local analytical tests that can applied independently to any point or cell in a vector field. These techniques draw on concepts from critical point theory and phase plane analysis and utilize the velocity gradient tensor. For this 3x3 tensor an eigen-analysis produces 3 eigenvalues. Mapping these to the complex plane produces the classification signature. Vector field topology can be used as the foundation of automated fluid feature extraction.