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

TL;DR

This paper develops a new self-sustaining process theory explaining the formation of uniform momentum zones and internal shear layers in high Reynolds number shear flows, emphasizing inviscid dynamics and large-scale flow organization.

Contribution

It introduces a large-Reynolds-number asymptotic analysis revealing a mechanism for the formation of UMZs and shear layers via a three-dimensional instability of embedded shear layers.

Findings

Identifies a three-dimensional instability that sustains large-scale flow structures.

Provides a mechanistic explanation for UMZ formation in high Reynolds number flows.

Highlights the role of inviscid dynamics in flow self-organization.

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 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.