Tracking of vortices in a turbulent boundary layer

Abstract

AbstractThe motion of spanwise vortical elements and large-scale bulges has been tracked in the outer region between wall-normal distance $z/ \delta = 0. 11$ and 0.30 of a turbulent boundary layer at ${\mathit{Re}}_{\theta } = 2460$. The experimental dataset of time-resolved three-dimensional velocity fields used has been obtained by tomographic particle image velocimetry. The tracking of these structures yields their respective average trajectories as well as the variations thereof, quantified by the root mean square of the trajectory coordinates as a function of time. It is demonstrated that the variation in convection can be described by a dispersion model for infinitesimal particles in homogeneous turbulence, which suggests that these vortical structures and bulges are transported passively by the external velocity field without significant changes in their topology, at least over the present observation time of $1. 2\delta / {U}_{e} $. However, this does not mean that the structure’s convection velocity is equal to the local flow velocity at each instant. Differences of the order of the Kolmogorov or wall friction velocity have been observed for the spanwise vortical elements. In addition, the simultaneous detection and tracking of multiple structures allows an evaluation of the relative velocity between two spanwise vortex elements, which are approximately aligned along the streamwise direction. The typical streamwise distance between such neighbouring structures is found to be around $0. 2\delta $. Their relative velocities are small, especially the streamwise component, which shows less variation as may be expected based on the relative flow velocity statistics for the same separation distance. This appears consistent with the hairpin packet model, which comprises a set of streamwise aligned hairpins travelling coherently. In exceptional cases, however, the structures approach each other rapidly, forcing an interaction on a time scale of the order of $1\delta / {U}_{e} $. It is shown that the measured variation in convection velocity can further be used successfully to predict the temporal development of space–time correlation functions starting from the instantaneous correlation map. In this prediction the structures are assumed to convect without change, following our observations.