New criteria to detect singularities in experimental incompressible 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 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.
Keywords
Cite
@article{arxiv.1601.03922,
title = {New criteria to detect singularities in experimental incompressible flows},
author = {Denis Kuzzay and Ewe-Wei Saw and Fabio J. W. A. Martins and Davide Faranda and Jean-Marc Foucaut and François Daviaud and Bérengère Dubrulle},
journal= {arXiv preprint arXiv:1601.03922},
year = {2017}
}