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A mechanism for streamwise localisation of nonlinear waves in shear flows

Published online by Cambridge University Press:  17 August 2015

Fernando Mellibovsky  and
Alvaro Meseguer
Fernando Mellibovsky*
Affiliation:
Castelldefels School of Telecom and Aerospace Engineering, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain
Alvaro Meseguer
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain
*
†Email address for correspondence: [email protected]
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Abstract

We present the complete unfolding of streamwise localisation in a paradigm of extended shear flows, namely two-dimensional plane Poiseuille flow. Exact solutions of the Navier–Stokes equations are computed numerically and tracked in the streamwise wavenumber–Reynolds number parameter space to identify and describe the fundamental mechanism behind streamwise localisation, a ubiquitous feature of shear flow turbulence. Unlike shear flow spanwise localisation, streamwise localisation does not follow the snaking mechanism demonstrated for plane Couette flow.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Instability: Instability Turbulent Flows: Turbulent transition
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 779 , 25 September 2015 , R1
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Copyright
© 2015 Cambridge University Press 

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Mellibovsky et al. supplementary movie

Tollmien Schlichting wave at Re=2800.

Download Mellibovsky et al. supplementary movie(Video)
Video 16.2 MB

Mellibovsky et al. supplementary movie

Tollmien Schlichting wave at Re=2800.

Download Mellibovsky et al. supplementary movie(Video)
Video 1.2 MB

Mellibovsky et al. supplementary movie

Modulated Tollmien Schlichting wave at Re=2800

Download Mellibovsky et al. supplementary movie(Video)
Video 17.7 MB

Mellibovsky et al. supplementary movie

Modulated Tollmien Schlichting wave at Re=2800

Download Mellibovsky et al. supplementary movie(Video)
Video 1.3 MB

Mellibovsky et al. supplementary movie

Localised modulated Tollmien Schlichting wave at Re=2800.

Download Mellibovsky et al. supplementary movie(Video)
Video 11.4 MB

Mellibovsky et al. supplementary movie

Localised modulated Tollmien Schlichting wave at Re=2800.

Download Mellibovsky et al. supplementary movie(Video)
Video 932.1 KB