Growth of Nonlinear Patterns in Binary-Fluid Convection, Analysis of Models

Abstract

A recently proposed “minimal model” of the convection of binary mixtures in a Rayleigh–Bénard cell of aspect ratio 2 with realistic boundary conditions is invoked to study the transient dynamics from the entirely diffusive ground state to the convection state. The model was designed to reproduce the subcritical Hopf bifurcation found for negative Soret coupling in finite-difference simulations and experiments, but also performs well for the growth transients, including the competition between two counter-propagating waves. We prepared an initial state with only one wave, thus avoiding complicated wave competition. This allows us to elucidate the interaction of the concentration field with the pure-fluid fields, i.e., temperature and velocity, by means of modulus and phase equations. We explain the linear and nonlinear transient dynamics responsible for the strong decrease in frequency and concentration, and the feed-back loop responsible for propagation.