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
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Cited by in corpus (11)

• Statistical transition to turbulence in plane channel flow
• Crisis bifurcations in plane Poiseuille flow
• Exact coherent structures in two-dimensional turbulence identified with convolutional autoencoders
• Dynamics of laminar and transitional flows over slip surfaces: effects on the laminar-turbulent separatrix
• Self-sustainment of coherent structures in counter-rotating Taylor-Couette flow
• Direct path from turbulence to time-periodic solutions
• 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
• The twisted baker map
• Bifurcation structure of unstable periodic orbits in plane Couette flow with the Smagorinsky model