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

Published online by Cambridge University Press:  02 September 2020

Brandon Montemuro
Affiliation:
Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH03824, USA
Christopher M. White
Affiliation:
Department of Mechanical Engineering, University of New Hampshire, Durham, NH03824, USA
Joseph C. Klewicki
Affiliation:
Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH03824, USA Department of Mechanical Engineering, University of New Hampshire, Durham, NH03824, USA Department of Mechanical Engineering, University of Melbourne, Melbourne, Victoria3010, Australia
Gregory P. Chini*
Affiliation:
Program in Integrated Applied Mathematics, University of New Hampshire, Durham, NH03824, USA Department of Mechanical Engineering, University of New Hampshire, Durham, NH03824, USA
*
Email address for correspondence: greg.chini@unh.edu

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.

Type
JFM Papers
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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