Crisis bifurcations in plane Poiseuille flow

TL;DR

This paper investigates crisis bifurcations in plane Poiseuille flow, revealing how these bifurcations lead to complex, chaotic dynamics and transitions between different flow states through direct numerical simulations.

Contribution

It provides a detailed analysis of exterior and interior crisis bifurcations in transitional plane Poiseuille flow within a symmetric subspace, linking bifurcations to increased dynamical complexity.

Findings

Identification of exterior and interior crisis bifurcations in flow dynamics

Observation of intermittent behavior during interior crises

Transition from attractor to chaotic saddle at critical Reynolds numbers

Abstract

Many shear flows follow a route to turbulence that has striking similarities to bifurcation scenarios in low-dimensional dynamical systems. Among the bifurcations that appear, crisis bifurcations are important because they cause global transitions between open and closed attractors, or indicate drastic increases in the range of the state space that is covered by the dynamics. We here study exterior and interior crisis bifurcations in direct numerical simulations of transitional plane Poiseuille flow in a mirror-symmetric subspace. We trace the state space dynamics from the appearance of the first three-dimensional exact coherent structures to the transition from an attractor to a chaotic saddle in an exterior crisis. For intermediate Reynolds numbers, the attractor undergoes several interior crises, in which new states appear and intermittent behavior can be observed. The bifurcations contribute to increasing the complexity of the dynamics and to a more dense coverage of state space.