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arXiv · 1601.03922

New criteria to detect singularities in experimental incompressible flows

Denis Kuzzay·Ewe-Wei Saw·Fabio J. W. A. Martins·Davide Faranda·Jean-Marc Foucaut·François Daviaud·Bérengère Dubrulle
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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.

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Denis Kuzzay, Ewe-Wei Saw, Fabio J. W. A. Martins, Davide Faranda, Jean-Marc Foucaut, François Daviaud, Bérengère Dubrulle. 2016-01-15. New criteria to detect singularities in experimental incompressible flows. https://doi.org/10.1088/1361-6544%2Faa6aaf

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