Formation of coherent hairpin packets in wall turbulence

Experimental studies of wall turbulence using particle image velocimetry give clear evidence that inclined hairpin vortices are the dominant structure. Experimentally the hairpins are not perfectly symmetric, but they characteristically have pronounced arches or heads that make them more like a hairpin than a simple inclined, quasi-streamwise vortex. In the first layer adjacent to the wall these vortices occur in coherently organized packets in which they are aligned approximately behind one another, as in the conceptual models of Bandyopadhyay (1980) and Smith (1984). Within the envelope of a hairpin packet, the streamwise momentum is low, forming low speed regions that extend several hundred viscous length scales above the wall, and thousands of viscous length scales in the streamwise direction. Fully resolved numerical simulations of the evolution of a viscous hairpin vortex in Re_τ=180 channel flow have been performed to understand the mechanisms which can form packets of hairpins. The initial condition for the simulation is a stochastic estimate of the vector field surrounding an ejection event. The simulation reveals a mechanism for self-sustaining wall turbulence which unifies several earlier models and defines conditions under which it can occur. Above a critical level of the hairpin vortex strength relative to the background mean turbulent flow, the initial vortex spawns new hairpin vortices both upstream and downstream. To the sides, it creates quasi-streamwise vortices similar to those observed by Brooke and Hanratty (1993), and Bernard, Thomas and Handler (1993). Below the critical level, the vortex gradually dissipates.