Transition to turbulence in shear flows

TL;DR

This paper reviews recent advances in understanding the transition to turbulence in shear flows, focusing on linear and nonlinear states, pattern formation, and spatio-temporal dynamics related to directed percolation.

Contribution

It summarizes recent progress in understanding shear flow turbulence transition, emphasizing the roles of linear/nonlinear states and spatio-temporal dynamics.

Findings

Identification of key linear and nonlinear states driving transition

Observation of extended and localized turbulent patterns

Connection between turbulence dynamics and directed percolation

Abstract

Pipe flow and many other shear flows show a transition to turbulence at flow rates for which the laminar profile is stable against infinitesimal perturbations. In this brief review the recent progress in the understanding of this transition will be summarized, with a focus on the linear and nonlinear states that drive the transitions, the extended and localized patterns that appear, and on the spatio-temporal dynamics and their relation to directed percolation.