Streamwise and doubly-localised periodic orbits in plane Poiseuille flow

Abstract

We study localised exact coherent structures in plane Poiseuille flow that are relative periodic orbits. They are obtained from extended states in smaller, periodically continued domains, by increasing the length to obtain streamwise localization and then by increasing the width to achieve spanwise localisation. The states maintain the travelling wave structure of the extended states, which is then modulated by a localised envelope on larger scales. In streamwise direction, the envelope shows exponential localization, with different exponents on the upstream and downstream side. The upstream exponent increases linearly with Reynolds number Re, but the downstream exponent is essentially independent of Re. In the spanwise direction the decay is compatible with a power-law localisation. As the width increases the localised state undergoes further bifurcations which add additional unstable directions, so that the edge state the relative attractor on the boundary between the laminar and turbulent motions, in the system becomes chaotic.

Revision

References in corpus (7)

• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Lower branch coherent states in shear flows: transition and control
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• Turbulent-laminar patterns in plane Poiseuille flow
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Cited by in corpus (6)

• Crisis bifurcations in plane Poiseuille flow
• Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
• Localization in a spanwise-extended model of plane Couette flow
• Streamwise decay of localized states in channel flow
• A spotlike edge state in plane Poiseuille flow
• Bifurcation structure of unstable periodic orbits in plane Couette flow with the Smagorinsky model