Nonlinear pattern and wave-number selection in convecting binary mixtures.

Considerable efforts have recently been made to understand and identify various spatio-temporal transitions from an unstable state to a coherently oscillating or chaotic state in numerous hydrodynamic flows. Oscillatory convection in binary mixtures as well as a variety of open-flow systems show a transition to spatially developing traveling waves (TW). For these systems a generalized Ginzburg-Landau (GGL) equation can be derived as a simple model describing the nonlinear evolution of propagating patterns rp(a, +sa„)A (I+tcp)eA+ (I+'tc, )gpss„'A —g(1+ic2) )A ( A.