Spatiotemporal dynamics near the onset of convection for binary mixtures in cylindrical containers

Abstract

Pattern selection near the onset of convection in a cylindrical container heated from below is investigated numerically for a water-ethanol mixture, with parameter values and boundary conditions relevant to experiments. The Boussinesq three-dimensional equations for binary fluid convection are simulated for cylinders of aspect ratio Gamma=11 and 10.5 (Gamma identical with R/d, where R is the radius of the cell and d its height). The onset of convection occurs via a subcritical Hopf bifurcation in which the critical mode is strongly influenced by small variations of the aspect ratio of the cell. During the linear regime, an m=1 azimuthal mode consisting of radially traveling waves grows in amplitude in the Gamma=11 cell, while an m=0 azimuthal mode is selected in the Gamma =10.5 cylinder. As convection evolves, simulations for subcritical and supercritical Rayleigh numbers reveal differences in the dynamics. Very close to the critical value, convection is erratic and focuses along one or more diameters of the cell; growths and collapses of the convection amplitude take place, but convection eventually dies away for subcritical values and persists for slightly supercritical values. For larger supercritical values, convection grows progressively in amplitude, and patterns consist of traveling-wave regions of convection initially focused near the cell center, though expanding slowly until a large-amplitude state is reached. Depending on the reduced Rayleigh number, the final state can be a nonsteady state filling the cell or a disordered confined state.