Predicting the motion of phase defects in a traveling-wave convection pattern

Abstract

A phase equation paradigm is used to analyze traveling-wave patterns in convection in a binary mixture of ethanol and water. The complex order parameter of the traveling-wave pattern is calculated and phase defects are identified. The locations and charges of the phase defects in the pattern are used as the basis of a reconstruction of the phase field of the pattern. The reconstruction requires the adjustment of a single free parameter, the pitch of the defects. The reconstructed phase field is similar to the measured field, but has a wider spectrum of wave numbers, suggesting another mechanism, such as phase diffusion, is required to relax the reconstructed field to the measured field. It is found that the defect velocity is correlated with the phase gradient of the complex order parameter. This makes it possible to predict the motion of the defects, and by extension the evolution of the patterns.