Weakly Nonlinear Traveling-Wave States in Convection

Convection in binary fluid mixtures begins with a linear instability to a state of counter propagating traveling waves which is now quantitatively understood. This instability triggers a hysteretic transition to a nonlinear convective state which can be created. In this regime, the flow consists of one-dimensional, counterpropagating waves which are quite close to the linear states in spatial pattern and in oscillation frequency. The basic state consists of a confined region of traveling waves which slowly alternates from one side of the experimental cell to the other. Because the effects of nonlinearities are weak, and since the spatial pattern is so simple, this flow ought to be understandable in terms of a theory which considers the convection to be a small perturbation of the background motionless state. This is indeed the basis of the calculations of Cross, which reproduce many of the experimental observations.