Convection in binary fluid mixtures. I. Extended traveling-wave and stationary states

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Abstract
Nonlinear, spatially extended structures of convection rolls in horizontal layers of binary fluids heated from below are investigated in quantitative detail as a function of Rayleigh number for several negative and positive Soret coupling strengths (separation ratios) and different Lewis and Prandtl numbers characterizing different mixtures. A finite-difference method was used to solve the full hydrodynamic field equations in a vertical cross section perpendicular to the roll axes, subject to realistic horizontal and laterally periodic boundary conditions in a range of experimentally accessible parameters. We elucidate the important role that the concentration field plays in the structural dynamics of the nonlinear states of stationary overturning convection (SOC) and of traveling-wave (TW) convection investigated here. Structural differences in the concentration boundary layers and of the concentration plumes in TW’s and SOC’s and their physical consequences are discussed. These properties show that the states considered here are indeed strongly nonlinear, as expected from the magnitude of advection and diffusion in the concentration balance. The bifurcation behavior of the states is analyzed using different order parameters such as flow intensity, Nusselt number, a mixing parameter characterized by the variance of the concentration field, and the TW frequency. For further comparison with experiments, light intensity distributions are determined that can be observed in side-view shadowgraphs done with horizontal light along the roll axes.
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