The Lid-Driven Cavity's Many Bifurcations - A Study of How and Where They Occur

Abstract

Computational simulations of a two-dimensional incompressible regularized lid-driven cavity were performed and analyzed to identify the dynamic behavior of the flow through multiple bifurcations which ultimately result in chaotic flow. Pseudo-spectral numerical simulations were performed at Reynolds numbers from 1,000 to 25,000. Traditional as well as novel methods were implemented to characterize the system's behavior. The first critical Reynolds number, near 10,250, is found in agreement with existing literature. An additional bifurcation is observed near a Reynolds number of 15,500. The largest Lyapunov exponent was studied as a potential perspective on chaos characterization but its accurate computation was found to be prohibitive. Phase space and power spectrum analyses yielded comparable conclusions about the flow's progression to chaos. The flow's transition from quasi-periodicity to chaos between Reynolds numbers of 18,000 and 23,000 was observed to be gradual and of the form of a toroidal bifurcation. The concepts of frequency shredding and power capacity are introduced which, paired with an existing understanding of frequency entrainment, can help explain the system's progression through quasi-periodicity to chaos.