A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

Abstract Many exact coherent states (ECS) arising in wall-bounded shear flows have an asymptotic structure at extreme Reynolds number $Re$ in which the effective Reynolds number governing the streak and roll dynamics is $\mathit {O}(1)$. Consequently, these viscous ECS are not suitable candidates for quasi-coherent structures away from the wall that necessarily are inviscid in the mean. Specifically, viscous ECS cannot account for the singular nature of the inertial domain, where the flow self-organizes into uniform momentum zones (UMZs) separated by internal shear layers and the instantaneous streamwise velocity develops a staircase-like profile. In this investigation, a large-$Re$ asymptotic analysis is performed to explore the potential for a three-dimensional, short streamwise- and spanwise-wavelength instability of the embedded shear layers to sustain a spatially distributed array of much larger-scale, effectively inviscid streamwise roll motions. In contrast to other self-sustaining process theories, the rolls are sufficiently strong to differentially homogenize the background shear flow, thereby providing a mechanistic explanation for the formation and maintenance of UMZs and interlaced shear layers that respects the leading-order balance structure of the mean dynamics.