Local wave director analysis of domain chaos in Rayleigh–Bénard convection

We present new results both from numerical simulations using the Swift–Hohenberg model and from experiment for domain chaos near the onset of rotating Rayleigh–Bénard convection. Using both global Fourier analysis and local wave director (LWD) analysis, the domain chaos patterns were characterized. Several image analysis techniques are discussed and were applied to the director field obtained from LWD analysis. They yielded statistical parameters, averaged over long time series, that characterize several aspects of the chaotic patterns. The effect of the finite image size on the determination of the domain switching frequency obtained with Fourier analysis, as well as with LWD analysis, was investigated. Using the LWD method, we studied ξθ, a correlation length obtained from the time-averaged autocorrelation of the local angle field θ. The defects and domains in the pattern were examined locally and their average area fraction, average area, and average major axis length were obtained. A periodic component was observed in the time series of the instantaneous correlation length ξ̃θ and of the defect area, but was found not to be present in the time series of the domain area. We determined a parameter D, defined as the average dot product of the wave director and the major domain axis, that characterizes the orientation of the domains relative to the roll patterns within them. The results for D were independent of the control parameter ε and of the image size. Simulations and experiment gave remarkably similar results for D.