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Linear and nonlinear properties of convection in binary uid layers heated from below are investigated, in particular for gas parameters. A Galerkin approximation for realistic boundary conditions that describes stationary and oscillatory convection in the form of straight parallel rolls is used to determine the in uence of the Dufour e ect on the bifurcation behaviour of convective ow intensity, vertical heat current, and concentration mixing. The Dufour{induced changes in the bifurcation topology and the existence regimes of stationary and traveling wave convection are elucidated. To check the validity of the Galerkin results we compare with nite{ di erence numerical simulations of the full hydrodynamical eld equations. Furthermore, we report on the scaling behaviour of linear properties of the stationary instability.

A minimal, analytically manageable Galerkin type model for convection in binary mixtures subject to realistic boundary conditions is presented. The model elucidates and reproduces the typical bifurcation topology of extended stationary and oscillatory convective states seen for negative Soret coupling: backwards stationary and Hopf bifurcations, saddle node bifurcations to stable strongly nonlinear stationary and traveling wave (TW) states, and merging of the TW solution branch with stationary states. Also unstable standing wave solutions are obtained. A systematic analysis of the concentration balance for liquid mixture parameters has lead to a representation of the concentration field in terms of two linear and two nonlinear modes. This truncation captures the important large-scale effects in the laterally averaged concentration field resulting from advective and diffusive mixing. Also the fact that with increasing flow intensity along the TW solution branch the frequency decreases monotonically in the same way as the mixing increases -the variance of the concentration distribution decreases -is ensured and reproduced well. Universal scaling relations between flow intensity, frequency, and variance of the concentration distribution (degree of mixing) in a TW are predicted by the model and have been confirmed by numerical solutions of the full equations. The validity of the model is checked by comparison with numerical solutions of the full field equations. PACS number(s): 47.10.+g, 03.40.Gc

Convection in horizontal layers of binary fluids heated from below and in particular the influence of the Soret effect on the bifurcation properties of extended stationary and traveling patterns that occur for negative Soret coupling is investigated theoretically. The fixed points corresponding to these two convection structures are determined for realistic boundary conditions with a many mode Galerkin scheme for temperature and concentration and an accurate one mode truncation of the velocity field. This solution procedure yields the stable and unstable solutions for all stationary and traveling patterns so that complete phase diagrams for the different convection types in typical binary liquid mixtures can easily be computed. Also the transition from weakly to strongly nonlinear states can be analyzed in detail. An investigation of the concentration current and of the relevance of its constituents shows the way for a simplification of the mode representation of temperature and concentration field as well as for an analytically manageable few mode description.Comment: 30 pages, 12 figure

Spatially extended stationary and traveling states in the strongly nonlinear regime of convection in layers of binary fluid mixtures heated from below are described by a few-mode-model. It is derived from the proper hydrodynamic balance equations including experimentally relevant boundary conditions with a non-standard Galerkin approximation that uses numerically obtained, symmetry decomposed modes. Properties of the model are elucidated and compared with full numerical solutions of the field equations.