Vortex core detection: back to basics

Abstract

Analyzing vortices in fluid flows is an important and extensively studied problem. Visualization methods are an important tool, and vortex cores, including vortex-core axes, are frequently objects for which visualization is attempted. A robust definition of vortex-core axis has eluded researchers for a decade. This paper reviews the criteria described in some early papers, as well as recent papers that concentrate on issues of unsteady flows, and attempts to build on their ideas. In particular, researchers have proposed criteria that are desirable for a vortex-core axis that correspond to nonlocal properties, yet current extraction methods are all based on local properties. Analysis is presented to support the thesis that inaccuracies observed in some popular early methods are due to a mixture of frequencies in the flow field in vortical regions. Such mixtures occur in steady flows, as well as unsteady (time-varying) flows. Thus, the fact that the flows are unsteady is not necessarily the primary reason for inaccuracies recently observed in vortex analysis of such flows. It is hypothesized that time-varying (unsteady) flows tend to be more complex, hence tend to have mixed frequencies more often than steady flows. We further conjecture that an "effective" lack of Galilean invariance may occur in steady or unsteady flows, due to the interaction of low frequencies with high frequencies.