New criteria to detect singularities in experimental incompressible flows

TL;DR

This paper proposes two new criteria for detecting singularities in experimental incompressible flows using PIV data, enabling local detection of low-scaling exponent singularities without full volume velocity fields.

Contribution

The authors introduce novel singularity detection criteria based on DR and Eyink methods that work with planar PIV data, expanding detection capabilities in experimental flows.

Findings

Criteria effectively detect singularities with scaling exponent h ≤ 1/2.

Detection from planar PIV data is feasible without full 3D velocity fields.

DR and BKM criteria show strong correlation in high Reynolds number flows.

Abstract

We introduce two new singularity detection criteria based on the work of Duchon-Robert (DR) [J. Duchon and R. Robert, Nonlinearity, 13, 249 (2000)], and Eyink [G.L. Eyink, Phys. Rev. E, 74 (2006)] which allow for the local detection of singularities with scaling exponent $h\leqslant1/2$ in experimental flows, using PIV measurements. We show that in order to detect such singularities, one does not need to have access to the whole velocity field inside a volume but can instead look for them from stereoscopic particle image velocimetry (SPIV) data on a plane. We discuss the link with the Beale-Kato-Majda (BKM) [J.T. Beale, T. Kato, A. Majda, Commun. Math. Phys., 94, 61 (1984)] criterion, based on the blowup of vorticity, which applies to singularities of Navier-Stokes equations. We illustrate our discussion using tomographic PIV data obtained inside a high Reynolds number flow generated inside the boundary layer of a wind tunnel. In such a case, BKM and DR criteria are well correlated with each other.