Tracking of vortices in a turbulent boundary layer

Abstract

The motion of spanwise vortical elements and large-scale bulges has been tracked in the outer region between wall-normal distance z/δ = 0.11 and 0.30 of a turbulent boundary layer at Re θ = 2460. The experimental dataset of time-resolved threedimensional 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 1.2δ/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 0.2δ. 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 1δ/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.

Interfaces and internal layers in a turbulent boundary layer

“…We therefore conjecture that large scale regions on average grow slowly, i.e., with the same order of magnitude as the average boundary layer growth rate. Furthermore, it is worth mentioning that the boundary entrainment velocity of the average shear layer at y/δ 99 = 0.2 (E b ≈ 0.003U ∞ ) shows a correspondence with the work of Elsinga et al, 44 who found the average wall-normal convection velocity of spanwise vortices to be 0.006U e ± 0.002U e . Assuming these vortices populate the shear layers, this correspondence with the motion of instantaneous vortex structures supports the present conditional averaging approach.…”

Possible modification of the large-scale flow structures by vortical structural interactions

“…It can be observed that the swirling strength increases until ∆t + = 0, i.e, the time at which the event was specified, and then decreases steadily with increasing time. This decreasing strength corresponds to a loss of correlation with increasing time shifts, which can be attributed to variations in convection velocities of the structures considered in the averaging [3]. Similarly, figure 4 shows that the peak negative Reynolds shear stress, normalized by its value at ∆t + = 0, increases until ∆t + = 0 and then decreases.…”

“…They have also highlighted examples of vortex structures merging or splitting [2,3,8]. When presenting structural interactions, only the (small-scale) vortices were included in the discussion.…”

Resolving vorticity and dissipation in a turbulent boundary layer by tomographic PTV and VIC+

“…Following two decades of experimental and numerical work in wall-bounded turbulent flows, as reviewed in Marusic et al (2010), today's experiments by tomographic particle image velocimetry (PIV) have allowed for unprecedented volumetric and time-resolved measurement of such flows (Schröder et al 2008(Schröder et al , 2011Elsinga and Marusic 2010;Elsinga et al 2012). Recent studies have, however, stumbled upon the spatial resolution limitations of tomographic PIV for measurements in a turbulent flow (Atkinson et al 2011;Kähler et al 2012;Lynch et al 2014).…”