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

Abstract

We present new results both from numerical simulations using the Swift–Hohenberg modeland from experiment for domain chaos near the onset of rotating Rayleigh–Bénardconvection. Using both global Fourier analysis and local wave director (LWD) analysis, thedomain chaos patterns were characterized. Several image analysis techniques are discussedand were applied to the director field obtained from LWD analysis. They yielded statisticalparameters, averaged over long time series, that characterize several aspects of the chaoticpatterns. The effect of the finite image size on the determination of the domain switchingfrequency obtained with Fourier analysis, as well as with LWD analysis, was investigated.Using the LWD method, we studiedξθ, a correlation length obtained from the time-averaged autocorrelation of the local angle fieldθ. The defects and domains in the pattern were examined locally and their average areafraction, average area, and average major axis length were obtained. A periodic componentwas observed in the time series of the instantaneous correlation length and of the defect area, but was found not to be present in the time series of the domainarea. We determined a parameter , defined as the average dot product of the wave director and the major domain axis, thatcharacterizes the orientation of the domains relative to the roll patterns within them. Theresults for were independent of the control parameterε and of the image size. Simulations and experiment gave remarkably similar results for.