Studying edge geometry in transiently turbulent shear flows

Abstract

In linearly stable shear flows at moderate Re, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge of chaos, which separates decaying perturbations from those triggering turbulence. We statistically analyse the decay in plane Couette flow, quantify the breaking of self-sustaining feedback loops and demonstrate the existence of a whole continuum of possible decay paths. Drawing parallels with low-dimensional models and monitoring the location of the edge relative to decaying trajectories we provide evidence, that the edge of chaos separates state space not globally. It is instead wrapped around the turbulence generating structures and not an independent dynamical structure but part of the chaotic saddle. Thereby, decaying trajectories need not cross the edge, but circumnavigate it while unwrapping from the turbulent saddle.

11 pages, 6 figures

References in corpus (5)

• Turbulence transition and the edge of chaos in pipe flow
• Streamwise-localized solutions at the onset of turbulence in pipe flow
• Periodic orbits near onset of chaos in plane Couette flow
• Laminar-turbulent boundary in plane Couette flow
• Recurrence of Travelling Waves in Transitional Pipe Flow

Cited by in corpus (8)

• Extreme events in transitional turbulence
• Disruption of SSP/VWI states by a stable stratification
• An input-output inspired method for permissible perturbation amplitude of transitional wall-bounded shear flows
• The edge as a Lagrangian Coherent Structure in a high-dimensional state space
• A probabilistic protocol for the assessment of transition and control
• Edge state modulation by mean viscosity gradients
• Does rare, noise-induced, bypass transition in plane Couette flow bypass instantons ?
• Optimizing the control of transition to turbulence using a Bayesian method