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Mean flow of turbulent–laminar patterns in plane Couette flow
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Barkley, Dwight and Tuckerman, Laurette S.. (2007) Mean flow of turbulent–laminar patterns in plane Couette flow. Journal of Fluid Mechanics, Vol.57 . pp. 109137. ISSN 00221120

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Official URL: http://dx.doi.org/10.1017/S002211200600454X
Abstract
A turbulent–laminar banded pattern in plane Couette flow is studied numerically. This pattern is statistically steady, is oriented obliquely to the streamwise direction, and has a very large wavelength relative to the gap. The mean flow, averaged in time and in the homogeneous direction, is analysed. The flow in the quasilaminar region is not the linear Couette profile, but results from a nontrivial balance between advection and diffusion. This force balance yields a first approximation to the relationship between the Reynolds number, angle, and wavelength of the pattern. Remarkably, the variation of the mean flow along the pattern wavevector is found to be almost exactly harmonic: the flow can be represented via only three crosschannel profiles as U(x, y, z) ≈ U0(y) + Uc(y) cos(kz) + Us(y) sin(kz). A model is formulated which relates the crosschannel profiles of the mean flow and of the Reynolds stress. Regimes computed for a full range of angle and Reynolds number in a tilted rectangular periodic computational domain are presented. Observations of regular turbulent–laminar patterns in other shear flows – Taylor–Couette, rotor–stator, and plane Poiseuille – are compared.
Item Type:  Journal Article 

Subjects:  Q Science > QA Mathematics 
Library of Congress Subject Headings (LCSH):  Fluid dynamics, Laminar flow, Turbulence 
Journal or Publication Title:  Journal of Fluid Mechanics 
Publisher:  Cambridge University Press 
ISSN:  00221120 
Official Date:  28 March 2007 
Volume:  Vol.57 
Page Range:  pp. 109137 
Identification Number:  10.1017/S002211200600454X 
Status:  Peer Reviewed 
Access rights to Published version:  Open Access 
References:  Andereck, C. D., Liu, S. S. & Swinney, H. L. 1986 Flow regimes in a circular protect Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183. 
URI:  http://wrap.warwick.ac.uk/id/eprint/662 
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