Acceleration feature points of unsteady shear flows

Abstract

In this paper, we propose a novel framework to extract features such as vortex cores and saddle points in two-dimensional unsteady flows. This feature extraction strategy generalizes critical points of snapshot topology in a Galilean-invariant manner, allows to prioritize features according to their strength and longevity, enables to track the temporal evolution of features, is robust against noise and has no subjective parameters. These characteristics are realized via several constitutive elements. First, acceleration is employed as a feature identifier following Goto and Vassilicos (2006), thus ensuring Galilean invariance. Second, the acceleration magnitude is used as basis for a mathematically well-developed scalar field topology. The minima of this field are called acceleration feature points, a superset of the acceleration zeros. These points are discriminated into vortices and saddle points depending the spectral properties of the velocity Jacobian. Third, all operations are based on discrete topology for the scalar field with combinatorial algorithms. This parameter-free foundation allows (1) to use persistence as a physically meaningful importance measure to prioritize feature points, (2) ensures robustness since no differentiation and interpolation need to be performed with the data, and (3) enables a natural and robust tracking algorithm for the temporal feature evolution. In particular, we can track vortex merging events in an unsupervised manner. Data based analyses are presented for an incompressible periodic cylinder wake, an incompressible planar mixing layer and a weakly compressible planar jet. They demonstrate the power of the tracking approach, which provides a spatiotemporal hierarchy of the minima.