Bypass transition and subcritical turbulence in plane Poiseuille flow

TL;DR

This paper investigates the bypass transition to turbulence in plane Poiseuille flow, revealing how finite amplitude perturbations lead to chaotic dynamics and transient turbulence through bifurcations and crisis phenomena.

Contribution

It demonstrates the route to turbulence in plane Poiseuille flow via bifurcation analysis of a symmetric subspace, linking it to known phenomena in boundary layers and plane Couette flow.

Findings

Identification of a traveling wave as the edge state.

Observation of a boundary crisis leading to transient chaos.

Connection of bifurcation cascade to the transition process.

Abstract

Plane Poiseuille flow shows turbulence at a Reynolds number that is lower than the critical one for the onset of Tollmien-Schlichting waves. The transition to turbulence follows the same route as the by-pass transition in boundary layers, i.e. finite amplitude perturbations are required and the flow is dominated by downstream vortices and streaks in the transitional regime. In order to relate the phenomenology in plane Poiseuille flow to our previous studies of plane Couette flow (Kreilos & Eckhardt, 2012), we study a symmetric subspace of plane Poiseuille flow in which the bifurcation cascade stands out clearly. By tracing the edge state, which in this system is a travelling wave, and its bifurcations, we can trace the formation of a chaotic attractor, the interior crisis that increase the phase space volume affected by the flow, and the ultimate transition into a chaotic saddle in a crisis bifurcation. After the boundary crisis we can observe transient chaos with exponentially distributed lifetimes.