Transition to chaos for buoyant flows in a groove heated from below

In this paper, the transition to chaos for buoyant flows in a groove heated from below is analyzed using a three-dimensional numerical model. With a Prandtl number of 0.71 and an aspect ratio of 0.5, numerical simulations are performed for Rayleigh number Ra from 10(0) to 10(5). This wide range covers the transition process to chaos, the first change being the instability of the primary steady symmetric flow in the form of a symmetry-breaking pitchfork bifurcation between Ra = 1.5 x 10(3) and 1.6 x 10(3) that tilts the buoyant flow toward one or the other sidewall of the groove. A second pitchfork bifurcation to the three-dimensional flow occurs between Ra = 5.3 x 10(3) and 5.4 x 10(3). A Hopf bifurcation is observed between Ra = 5.6 x 10(3) and 5.7 x 10(3) at which the buoyant flow in the groove becomes temporally periodic; this is followed by a sequence of further bifurcations including period-doubling and quasi-periodic bifurcations. Finally, the buoyant flow becomes chaotic when bulge motion appears along the groove between Ra = 6.5 x 10(3) and 6.6 x 10(3). Limit points, limit cycles, attractors, maximum Lyapunov exponents, and power spectral density are presented to analyze typical buoyant flows in the transition to chaos. Additionally, the heat and mass transfer is quantified for the different regimes. Published under license by AIP Publishing.