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Rayleigh-Bénard convection in horizontal layers of binary fluid mixtures heated from below with realistic horizontal boundary conditions is studied theoretically using multimode Galerkin expansions. For positive separation ratios the main difference between the mixtures and pure fluids lies in the existence of stable three dimensional patterns near onset in a wide range of the parameter space. We evaluated the stationary solutions of roll, crossroll, and square convection and we determined the location of the stability boundaries for many parameter combinations thereby obtaining the Busse balloon for roll and square patterns.

The influence of an externally imposed lateral Poiseuille through flow on linear, nonlinear, and transient behavior of transverse convective rolls in a horizontal layer of binary fluids heated from below is investigated. The convective roll solutions are determined numerically for realistic boundary conditions with a many-mode Galerkin expansion as well as with a finite-difference method. Bifurcation diagrams of various quantities like Nusselt number, frequency, and mixing behavior are determined as functions of heating rate and wave number for several through flow rates and Soret coupling strengths for ethanol-water parameters. The growth dynamics of small convective perturbations into different, strongly nonlinear convective states and the transition between the latter is studied also.

Dynamics and structure of spatially localized convective perturbations in binary fluid layers heated from below and the effect of a plane horizontal Poiseuille throughflow on them are investigated. Fronts and pulse-like wave packets formed out of the three relevant perturbations-two oscillatory ones and a stationary one-are analyzed after evaluating the appropriate saddle points of the three respective dispersion relations of the linear field equations over the complex wave number plane. Front and pulse properties are elucidated in quantitative detail as a function of small throughflow Reynolds numbers for different Soret coupling strengths psi including the pure fluid limit psi=0 in comparison with the appropriate Ginzburg-Landau amplitude equation approximations. Furthermore, small amplitude pulses and fronts obtained from solving the full nonlinear field equations numerically are presented to check and compare with the linear results.