Convection in Binary Fluid Mixtures. I. Extended Traveling Wave and Stationary States. (Physical Review E, in press)

Abstract

Nonlinear convection structures 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 range of experimentally accessible parameters. We elucidate the important role that the concentration field plays in the nonlinear states of stationary overturning convection (SOC) and of traveling wave (TW) convection. 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 con- sidered here are indeed strongly nonlinear, as expected from the magnitude of advection and diffusion in the concentration balance. The bifurcation behaviour of the states is analysed using different order parameters such as flow intensity, Nusselt number, a newly defined 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. Structural analyses of all fields are made using colour coded isoplots, vertical and lateral field profiles, and lateral Fourier decompositions. Transport properties of TWs are also discussed, in particular the mean lateral concentration current that is caused by the phase difference between concentration wave and velocity wave and that is roughly proportional to the TW frequency. This current plays an important role in the structural dynamics and stability of spatially-localized traveling-wave convection (cf. accompanying paper).