BYPASS TRANSITION AND SUBCRITICAL TURBULENCE IN PLANE POISEUILLE FLOW

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.