New method for detecting singularities in experimental incompressible flows

• Published in: Nonlinearity Vol. 30; no. 6; pp. 2381 - 2402
• Main Authors: Kuzzay, Denis, Saw, Ewe-Wei, Martins, Fabio J W A, Faranda, Davide, Foucaut, Jean-Marc, Daviaud, François, Dubrulle, Bérengère
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.06.2017
• Subjects: Duchon-Robert; energy dissipation; Fluid mechanics; inertial dissipation; Mechanics; Navier-Stokes; Onsager's conjecture; Physics; singularity; turbulence
• ISSN: 0951-7715; 1361-6544
• DOI: 10.1088/1361-6544/aa6aaf

We introduce two new criteria based on the work of Duchon and Robert (2000 Nonlinearity 13 249) and Eyink (2006 Phys. Rev. E 74 066302), which allow for the local detection of Navier-Stokes singularities in experimental flows. We discuss the difference between non-dissipative or dissipative Euler quasi-singularities and genuine Navier-Stokes dissipative singularites, and classify them with respect to their Hölder exponent h. We show that our criteria allow us to detect areas in a flow where the velocity field is no more regular than Hölder continuous with some Hölder exponent h⩽1/2. We illustrate our discussion using classical tomographic particle image velocimetry (TPIV) measurements obtained inside a high Reynolds number flow generated in the boundary layer of a wind tunnel. Our study shows that, in order to detect singularities or quasi-singularities, one does not need to have access to the whole velocity field inside a volume, but can instead look for them from stereoscopic PIV data on a plane. We also provide a discussion about the link between areas detected by our criteria and areas corresponding to large vorticity. We argue that this link might provide either a clue about the genesis of these quasi-singularities or a way to discriminate dissipative Euler quasi-singularities and genuine Navier-Stokes singularities.