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.

Flowtrace: simple visualization of coherent structures in biological fluid flows

“…Thus, plotting a scalar field from PIV (like vorticity) may be preferable when the time scale of particle advection within the field of view is comparable to the time scale of flow variation. A similar argument would apply to other common scalars computed as the finite differences of PIV data, such as the strain and shear (Colin et al, 2010;Kiørboe and Visser, 1999), as well as more sophisticated techniques based on computing Eulerian quantities like the local acceleration (Kasten et al, 2011;Van Gelder, 2012). For example, at high Reynolds number, vorticity is conserved and remains localized, causing patches of vorticity that remain intact as they are advected by the flow.…”

The State of the Art in Vortex Extraction

“…swirling can be found in boundary layers. Kenwright and Haimes [KH97] and Van Gelder [VG12] made aware that inaccurate results with local methods are not only attributed to (possible) lack of Galilean invariance, but also arise when swirling occurs at different scales. Thus, if the aerodynamics at a specific location is a sum of several effects (vortices at different scales [VG12] or a general bending of the coreline [RP96]), local methods will depend on the strongest effect and the extracted coreline will be displaced to some degree.…”

“…swirling can be found in boundary layers. Kenwright and Haimes [KH97] and Van Gelder [VG12] made aware that inaccurate results with local methods are not only attributed to (possible) lack of Galilean invariance, but also arise when swirling occurs at different scales. Thus, if the aerodynamics at a specific location is a sum of several effects This illustration is from [SWTH07].…”

“…(vortices at different scales [VG12] or a general bending of the coreline [RP96]), local methods will depend on the strongest effect and the extracted coreline will be displaced to some degree.…”

Computational and Theoretical Analyses of the Precessing Vortex Rope in a Simplified Draft Tube of a Scaled Model of a Francis Turbine

“…Similarly, if u and e are the velocity vector and the real eigenvector of D, then the real eigen helicity is defined as h ¼ ðu Á eÞ (27) For a detailed description of visualization techniques for vortex ropes, see Refs. [37][38][39][40]. Figure 5 shows the vortex rope formed in the draft tube at t ¼ 10 s, visualized by all the methods described previously, for a discharge coefficient of 0.34.…”