Nonlinear Convective States in a Fluid Mixture with Through-Flow

We report a numerical study on traveling-wave convection in a binary fluid mixture with a laterally imposed weak through-flow. Nonlinear convective states were determined by solving two-dimensional basic hydrodynamic field equations subject to nonperiodic lateral boundary conditions. This system has previously been found to exhibit repeated and coexisting dynamical states for a channel with small aspect ratio. We study the patterns observed in channels with large aspect ratio and the influence of the aspect ratio on convection evolution. In long channels, traveling waves in one convective cycle have sufficient space to relax in the downstream region, while in short channels, the system appears to exert some stabilizing influence on traveling waves. This causes the critical Rayleigh number (at which the convective pattern makes a transition from one type to another) to depend on the aspect ratio. It is also found that the cycle periods of repeated evolution are not determined simply by the linear growth rates of convective perturbations, but are influenced greatly by the length of the convection channel.