Rare backflow and extreme wall-normal velocity fluctuations in near-wall turbulence

Abstract

Rare negative streamwise velocities and extreme wall-normal velocity fluctuations near the wall are investigated for turbulent channel flow at a series of Reynolds numbers based on friction velocity up to Re τ = 1000. Probability density functions of the wall-shear stress and velocity components are presented as well as joint probability density functions of the velocity components and the pressure. Backflow occurs more often (0.06% at the wall at Re τ = 1000) and further away (up to y + = 8.5) from the wall for increasing Reynolds number. The regions of backflow are circular with an average diameter, based on ensemble averages, of approximately 20 viscous units independent of Reynolds number. A strong oblique vortex outside the viscous sublayer is found to cause this backflow. Extreme wall-normal velocity events occur also more often for increasing Reynolds number. These extreme fluctuations cause high flatness values near the wall (F(v) = 43 at Re τ = 1000). Positive and negative velocity spikes appear in pairs, located on the two edges of a strong streamwise vortex as documented by Xu et al. [Phys. Fluids 8, 1938 (1996)] for Re τ = 180. The spikes are elliptical and orientated in streamwise direction with a typical length of 25 and a typical width of 7.5 viscous units at y + ≈ 1. The negative spike occurs in a high-speed streak indicating a sweeping motion, while the positive spike is located in between a high and low-speed streak. The joint probability density functions of negative streamwise and extreme wall-normal velocity events show that these events are largely uncorrelated. The majority of both type of events can be found lying underneath a large-scale structure in the outer region with positive sign, which can be understood by considering the more intense velocity fluctuations due to amplitude modulation of the inner layer by the outer layer. Simulations performed at different resolutions give only minor differences. Results from experiments and recent turbulent boundary layer simulations show similar results indicating that these rare events are universal for wall-bounded flows. In order to detect these rare events in experiments, measurement techniques have to be specifically tuned.

Wall shear stress fluctuations: Mixed scaling and their effects on velocity fluctuations in a turbulent boundary layer

“…Insufficient resolution of experimental data has sometimes led to suggest that there are no flow reversals at the wall, τ x < 0 [8,46]. However, the present results confirm a small non-zero probability for extreme events where τ x < 0, in the order of 5 × 10 −4 , as shown in Table I, which is consistent with previous numerical studies [15,25]. The relation between the components of the instantaneous shear stress vector τ (t) =…”

“…If these passing quasi-streamwise vortices are tilted with respect to the x direction, they can induce small negative fluctuations to the streamwise component of the wall shear-stress. These kind of structures, also suggested by Lenaers et al [25], may explain the negative events of τ x and the yaw angle statistics.…”

Analysis of hot-wire measurements accuracy in turbulent boundary layer

“…Despite the predominant motion of the streamwise direction, the vortical structure that is present in a turbulent boundary layer has to act on the probe wire, inducing an uy velocity component. This was con rmed by the DNS study of Lenaers et al [5] who observed the high value of wall-normal velocity uctuations, which occasionally occur in the near-wall region and have larger magnitude than their local standard deviation.…”

Lagrangian wall shear stress structures and near-wall transport in high-Schmidt-number aneurysmal flows

“…Also, the structure of WSS lines have been used in developing theories for flow separation using dynamical system methods (Surana et al 2006(Surana et al , 2008. Recently, WSS critical points associated with rare near wall backflow have been observed in turbulent channel flows (Lenaers et al 2012;Brücker 2015). WSS patterns have been demonstrated to affect the heat transfer in impinging jets.…”