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

Published online by Cambridge University Press:  21 February 2020

Simon J. Illingworth Open the ORCID record for Simon J. Illingworth [Opens in a new window]
Simon J. Illingworth*
Affiliation:
Mechanical Engineering, University of Melbourne, VIC 3010, Australia
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Turbulent Flows: Turbulence modelling Turbulent Flows: Shear layer turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 889 , 25 April 2020 , A13
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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