Abstract
The regeneration and dynamics of near-wall longitudinal vortices – which dominate turbulence production, drag, and heat transfer – are analyzed using direct numerical simulation of turbulent channel flow. These dominant streamwise vortices are shown to result from nonlinear saturation of an instability of lifted low-speed streaks near a single wall, free from any initial vortex. The newly-found instability mechanism initiates streak waviness in the (x,z) plane, generating streamwise vorticity sheets. Streak waviness in turn induces positive ∂u/∂x (i.e. positive VISA), which causes these sheets' vorticity to then concentrate via stretching (rather than roll up) into new streamwise vortices. The instability requires sufficiently strong streaks (y circulation per unit x > 7.6 wall units) and is inviscid in nature, despite the close proximity of the no-slip wall. We find that self-annihilation of streaks due to viscous cross-diffusion of opposite-signed wall normal vorticity across each streak causes the instability amplification to scale in wall units, suggesting the relevance of our results to high Re as well. Significantly, the strongly 3D vortices generated by streak instability agree well with the CS educed from fully turbulent flow, suggesting the prevalence of this streak instability-based vortex formation mechanism. Simultaneous to vortex generation, an internal shear layer is generated across the streak from each streamwise vortex by stretching of spanwise vorticity. Such a shear layer eventually rolls up at the downstream end of a streamwise vortex, and the two link up and propagate outward to form a spanwise "arch" vortex. The newly generated streamwise vortices act to sustain/strengthen the preexisting streak which spawned them through localized lifting of near-wall fluid by induction. We develop a new spatiotemporal vortex generation mechanism, in which vortices leave behind "vortex-less" streaks, whose instability, due to the mechanism explained herein, initiates streamwise vortex formation.