Mechanism for turbulence proliferation in subcritical flows

TL;DR

This paper introduces a novel dynamical mechanism for puff proliferation in subcritical flows, explaining how turbulent structures split and validating it through simulations, with implications for turbulence transition theories.

Contribution

It proposes the first dynamical mechanism for puff splitting in pipe flow, including the concept of a split-edge state and its validation via numerical simulations.

Findings

Validated the puff splitting mechanism with numerical simulations

Predicted the form of the split-edge state

Discussed suppression of splits at higher Reynolds numbers

Abstract

The subcritical transition to turbulence, as occurs in pipe flow, is believed to generically be a phase transition in the directed percolation universality class. At its heart is a balance between the decay rate and proliferation rate of localized turbulent structures, called puffs in pipe flow. Here we propose the first-ever dynamical mechanism for puff proliferation -- the process by which a puff splits into two. In the first stage of our mechanism, a puff expands into a slug. In the second stage, a laminar gap is formed within the turbulent core. The notion of a split-edge state, mediating the transition from a single puff to a two puff state, is introduced and its form is predicted. The role of fluctuations in the two stages of the transition, and how splits could be suppressed with increasing Reynolds number, are discussed. Using numerical simulations, the mechanism is validated within the stochastic Barkley model. Concrete predictions to test the proposed mechanism in pipe and other wall bounded flows, and implications for the universality of the directed percolation picture, are discussed.