Oblique stripe solutions of channel flow

With decreasing Reynolds number, $Re$ , turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here the existence of localised nonlinear travelling wave solutions of the Navier–Stokes equations possessi...

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Bibliographic Details
Published inJournal of fluid mechanics Vol. 897
Main Authors Paranjape, Chaitanya S., Duguet, Yohann, Hof, Björn
Format Journal Article
LanguageEnglish
Published Cambridge Cambridge University Press 25.08.2020
Cambridge University Press (CUP)
Subjects
Bifurcations
Boundary conditions
Channel flow
Computational fluid dynamics
Flow stability
Fluid flow
Interfaces
Kinematics
Localization
Navier-Stokes equations
Nonlinear Sciences
Obliqueness
Orbits
Reynolds number
Robustness (mathematics)
Studies
Tracking
Traveling waves
Turbulence
Turbulent flow
Velocity
Vortices
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Summary:With decreasing Reynolds number, $Re$ , turbulence in channel flow becomes spatio-temporally intermittent and self-organises into solitary stripes oblique to the mean flow direction. We report here the existence of localised nonlinear travelling wave solutions of the Navier–Stokes equations possessing this obliqueness property. Such solutions are identified numerically using edge tracking coupled with arclength continuation. All solutions emerge in saddle-node bifurcations at values of $Re$ lower than the non-localised solutions. Relative periodic orbit solutions bifurcating from branches of travelling waves have also been computed. A complete parametric study is performed, including their stability, the investigation of their large-scale flow, and the robustness to changes of the numerical domain.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2020.322