Studying edge geometry in transiently turbulent shear flows. (23rd April 2014)

• Record Type: Journal Article
• Authors: Chantry, Matthew; Schneider, Tobias M.
• Is Part Of: Journal of fluid mechanics. Volume 747(2014:May)
• Page Start: 506
• Page End: 517
• Publication Date: 2014-04-23
• Subjects: instability, -- nonlinear dynamical systems, -- transition to turbulence; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2014.150
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract: In linearly stable shear flows at moderate Reynolds number, turbulence spontaneously decays despite the existence of a codimension-one manifold, termed the edge, 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 does not separate state space 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.