Direct path from turbulence to time-periodic solutions

Abstract

Viscous flows through pipes and channels are steady and ordered until, with increasing velocity, the laminar motion catastrophically breaks down and gives way to turbulence. How this apparently discontinuous change from low- to high-dimensional motion can be rationalized within the framework of the Navier--Stokes equations is not well understood. Exploiting geometrical properties of transitional channel flow we trace turbulence to far lower Reynolds numbers (Re) than previously possible and identify the complete path that reversibly links fully turbulent motion to an invariant solution. This precursor of turbulence destabilizes rapidly with Re, and the accompanying explosive increase in attractor dimension effectively marks the transition between deterministic and de facto stochastic dynamics.

arXiv commentTo be published in Physical Review Letters. 5 pages with 4 figures + supplemental material with 6 figures

References in corpus (21)

• Practical implementation of nonlinear time series methods: The TISEAN package
• The Significance of Simple Invariant Solutions in Turbulent Flows
• Recurrent motions within plane Couette turbulence
• Streamwise-localized solutions at the onset of turbulence in pipe flow
• Transition in pipe flow: the saddle structure on the boundary of turbulence
• Periodic orbits near onset of chaos in plane Couette flow
• Relative periodic orbits form the backbone of turbulent pipe flow
• Scale invariance at the onset of turbulence in Couette flow
• Universal continuous transition to turbulence in a planar shear flow
• The Openpipeflow Navier--Stokes Solver
• Turbulent-laminar patterns in plane Poiseuille flow
• Bifurcations to turbulence in transitional channel flow
• Streamwise and doubly-localised periodic orbits in plane Poiseuille flow
• Coarse graining the state space of a turbulent flow using periodic orbits
• Statistical transition to turbulence in plane channel flow
• Crisis bifurcations in plane Poiseuille flow
• Capturing Turbulent Dynamics and Statistics in Experiments with Unstable Periodic Orbits
• The growth mechanism of turbulent bands in channel flow at low Reynolds numbers
• Flow Statistics in the Transitional Regime of Plane Channel Flow
• Linear instability of turbulent channel flow
• Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

Cited by in corpus (4)

• Spatial marching with subgrid-scale local exact coherent structures in non-uniformly curved channel flow
• The chimera revisited: Wall- and magnetically-bounded turbulent flows
• Large-scale streak instabilities of transitional channel flow
• Discontinuous transition to shear flow turbulence