MODEL FOR CONVECTION IN BINARY LIQUIDS

A minimal, analytically manageable Galerkin type model for convection in binary mixtures subject to realistic boundary conditions is present ed. The model elucidates and reproduces the typical bifurcation topolo gy Of extended stationary and oscillatory convective states seen for n egative Soret coupling: backwards stationary and Hopf bifurcations, sa ddle node bifurcations to stable strongly nonlinear stationary and tra veling wave (TW) states, and merging of the TW solution branch with st ationary states. Also unstable standing wave solutions are obtained. A systematic analysis of the concentration balance for liquid mixture p arameters has led to a representation of the concentration field in te rms of two linear and two nonlinear modes. This truncation captures th e important large-scale effects in the laterally averaged concentratio n field resulting from advective and diffusive mixing. Also the fact t hat with increasing flow intensity along the TW solution branch the fr equency decreases monotonically in the same way as the mixing increase s-the variance of the concentration distribution decreases-is ensured and reproduced well. Universal scaling relations between flow intensit y, frequency, and variance of the concentration distribution (degree o f mixing) in a TW are predicted by the model and have been confirmed b y numerical solutions of the full equations. The validity of the model is checked by comparison with numerical solutions of the full field e quations.