The velocity and acceleration signatures of small-scale vortices in turbulent channel flow

Time-resolved particle-image velocimetry measurements are made in the streamwise-wall-normal plane of turbulent channel flow at Re-tau = 550 and 1747. Temporal and convective derivatives of velocity are computed from this data in order to evaluate the small-scale behaviour of these quantities as well as of the velocity itself. Instantaneous velocity fields indicate that the flow is dominated by small-scale vortex cores believed to be associated with hairpin/hairpin-like vortices. These vortices have been observed in realizations of the random velocity in other wall turbulence studies. In this work, a deterministic vortex signature is determined by conditional averaging techniques. This average signature is consistent with the hairpin vortex signature defined by Adrian and co-workers: circular streamlines with a strong ejection of low-speed fluid away from the wall (a Q(2) event) just upstream of the vortex head. In addition, the spatial extent of these small-scale vortices appears to remain relatively constant within the Reynolds-number range studied herein. Instantaneous time-derivative fields are spatially intermittent and are dominated by strong events that are spatially coincident with the small-scale vortex cores seen in the associated velocity fields. Stochastic estimation of the temporal derivative signature associated with the presence of a vortex core, coupled with Taylor's hypothesis considerations, shows that the small-scale vortices remain relatively frozen in time, implying that advective effects dominate the smaller spatial scales of the temporal derivative of velocity. The bulk convective derivative of velocity (i.e. the temporal derivative computed in a reference frame travelling at the bulk velocity) is found to be nearly an order of magnitude smaller than the temporal derivative of velocity. The vortex cores appear to rise away from the wall in the bulk convective frame, indicated by the positive wall-normal acceleration noted in the instantaneous bulk convective derivative fields. Stochastic estimation of the bulk convective derivative pattern associated with the presence of a vortex core confirms this behaviour.