Dynamics of two-dimensional traveling-wave convection patterns

We report an experimental study of traveling-wave convection patterns in a binary mixture of ethanol and water. We survey the patterns observed in a large aspect ratio cylindrical container over a broad range of Rayleigh numbers. It is found that disordered patterns observed immediately after traveling-wave convection is initiated evolve toward organized multidomain patterns and that the nature of the multidomain patterns depends on the Rayleigh number. A numerical algorithm for extracting the complex order parameter from traveling-wave patterns and measuring their dynamical properties is described. This technique is used to characterize the dynamic aspects of traveling-wave convection patterns observed near the saddle node bifurcation. It is shown that the instantaneous rate of deformation of the pattern can be determined, and use of this information as a point of comparison with model equations is discussed. The joint wave number, frequency distribution for traveling-wave patterns is calculated and is shown to be significantly different from the dispersion curves previously obtained from one-dimensional traveling-wave convection patterns. {} 1996 The American Physical Society.