Streamwise-constant large-scale structures in Couette and Poiseuille flows

The linear amplification mechanisms leading to streamwise-constant large-scale structures in laminar and turbulent channel flows are considered. A key feature of the analysis is that the Orr–Sommerfeld and Squire operators are each considered separately. Physically, this corresponds to considering t...

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Bibliographic Details
Published in:Journal of fluid mechanics 2020-04, Vol.889, Article A13
Main Author: Illingworth, Simon J.
Format: Article
Language:English
Subjects:
Amplification
Analysis
Channel flow
Computational fluid dynamics
Couette flow
Decomposition
Fluctuations
Fluid mechanics
Kinematics
Laminar flow
Profiles
Reynolds number
Structures
Velocity
Velocity distribution
Velocity profiles
Viscosity
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Summary:The linear amplification mechanisms leading to streamwise-constant large-scale structures in laminar and turbulent channel flows are considered. A key feature of the analysis is that the Orr–Sommerfeld and Squire operators are each considered separately. Physically, this corresponds to considering two separate processes: (i) the response of wall-normal velocity fluctuations to external forcing; and (ii) the response of streamwise velocity fluctuations to wall-normal velocity fluctuations. The analysis is performed for both plane Couette flow and plane Poiseuille flow; and for each we consider linear amplification mechanisms about both the laminar and turbulent mean velocity profiles. The analysis reveals two things. First, that the most amplified structures (with a spanwise spacing of approximately $4h$ , where $h$ is the channel half-height) are to an important degree encoded in the Orr–Sommerfeld operator alone, thus helping to explain their prevalence. Second – and consistent with numerical and experimental observations – that Couette flow is significantly more efficient than Poiseuille flow in leveraging the mean shear to produce channel-wide streamwise streaks.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2020.86