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 Reτ = 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 Reτ = 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 Reτ = 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)]10.1063/1.868973 for Reτ = 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.