Nonlinear dynamics in a backward-facing step flow

A numerical investigation has been conducted to explore the complex nonlinear nature of flow in a backward-facing step channel by the simulated results, which include the bifurcation diagram, limit cycle oscillations, power spectrums, and phase portraits. For small values of Reynolds number, the flow was steady and laminar. When the Reynolds number was amplified, the flow becomes unsteady with the initiation of a supercritical Hopf bifurcation. The flow path is trapped by the stable limit cycles, and this system is made to proceed with a sustained oscillation. As the Reynolds number was amplified further, the stability of the investigated system keeps decreasing through a sequence of frequency-doubling bifurcations. The fundamental frequency of high amplitude was identical to the most amplified mode of Kelvin-Helmholtz instability oscillations in the shear layer. Frequencies with a small amplitude result in a slower development of the Kelvin-Helmholtz instability and are responsible for the roll-up of the shear layer. The phase portrait shows the evolution of a chaotic attractor from a simple periodic attractor. Prior to the onset of the chaotic motion, pitchfork bifurcation showed its existence. (c) 2006 American Institute of Physics.