A self-sustaining process theory for uniform momentum zones and internal layers in wall turbulence

The instantaneous streamwise velocity in turbulent wall flows exhibits a staircase-like profile, with uniform momentum zones (UMZs) separated by internal layers of concentrated spanwise vorticity (termed `vortical fissures', or VFs) across which the streamwise flow speed jumps by a few multiples of the friction velocity. A fundamental challenge is to identify a mechanism that can account for observed properties of the UMZ/VF profiles while respecting the constraints imposed by the mean momentum balance. Specifically, measurements show that outboard of the near-wall peak in the Reynolds stress: (i) the characteristic VF thickness decreases as the friction Reynolds number Re_τ increases; and (ii) the mean momentum equation is inertially dominated. Supported by a new large-Re_τ asymptotic analysis of the Navier-Stokes equations, a multiple spatial scale self-sustaining process for UMZs and interlaced VFs is proposed that satisfies these two requirements.