New method for detecting singularities in experimental incompressible flows

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 Holder exponent h. We show that our criteria allow us to detect areas in a flow where the velocity field is no more regular than Holder continuous with some Holder exponent . 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.