Emergence of stochastic dynamics in plane Couette flow

TL;DR

This paper explores how stochastic and chaotic behaviors emerge in the dynamics of localized states in plane Couette flow, revealing the transition from deterministic to stochastic regimes below turbulence threshold.

Contribution

It demonstrates the existence of stochastic and chaotic transients in localized solutions of plane Couette flow, providing new insights into transition dynamics.

Findings

Identification of parameter intervals with stochastic dynamics

Observation of long-lived chaotic transients

Relaminarization dominated by deterministic dynamics

Abstract

Spatially localized states play an important role in transition to turbulence in shear flows (Kawahara, Uhlmann & van Veen, Annu. Rev. Fluid Mech. 44, 203 (2012)). Despite the fact that some of them are attractors on the separatrix between laminar and turbulent flows, little is known of their dynamics. We investigate here the temporal dynamics of such steady spatially localized solutions in the context of plane Couette flow. These solutions exist on oscillating branches in parameter space. We consider the saddle-nodes of these branches as initial conditions of simulations run with offset Reynolds numbers. We observe a relaminarization regime mostly characterized by deterministic dynamics and identify within this regime the existence of parameter intervals in which the results are stochastic and long-lived chaotic transients are observed. These results are obtained below the threshold for transition, shed light on the emergence of stochasticity in transitional plane Couette flow and will likely inform a range of shear flow configurations.