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Turbulent–laminar patterns in shear flows without walls

Published online by Cambridge University Press:  24 February 2016

Matthew Chantry ,
Laurette S. Tuckerman  and
Dwight Barkley
Matthew Chantry*
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636; PSL – ESPCI, Sorbonne Université – UPMC, Univ. Paris 06; Sorbonne Paris Cité – UDD, Univ. Paris 07, – 10 rue Vauquelin, 75005 Paris, France
Laurette S. Tuckerman
Affiliation:
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR CNRS 7636; PSL – ESPCI, Sorbonne Université – UPMC, Univ. Paris 06; Sorbonne Paris Cité – UDD, Univ. Paris 07, – 10 rue Vauquelin, 75005 Paris, France
Dwight Barkley
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
*
†Email address for correspondence: [email protected]
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Abstract

Turbulent–laminar intermittency, typically in the form of bands and spots, is a ubiquitous feature of the route to turbulence in wall-bounded shear flows. Here we study the idealised shear between stress-free boundaries driven by a sinusoidal body force and demonstrate quantitative agreement between turbulence in this flow and that found in the interior of plane Couette flow – the region excluding the boundary layers. Exploiting the absence of boundary layers, we construct a model flow that uses only four Fourier modes in the shear direction and yet robustly captures the range of spatiotemporal phenomena observed in transition, from spot growth to turbulent bands and uniform turbulence. The model substantially reduces the cost of simulating intermittent turbulent structures while maintaining the essential physics and a direct connection to the Navier–Stokes equations. We demonstrate the generic nature of this process by introducing stress-free equivalent flows for plane Poiseuille and pipe flows that again capture the turbulent–laminar structures seen in transition.

JFM classification

Nonlinear Dynamical Systems: Low-dimensional models Nonlinear Dynamical Systems: Pattern formation Instability: Transition to turbulence
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 791 , 25 March 2016 , R8
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Copyright
© 2016 Cambridge University Press 

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