Convection Patterns: Time Evolution of the Wave-Vector Field

Abstract

The evolution of Rayleigh-B\'enard convection patterns has been studied quantitatively with use of digital image processing methods to measure the time dependence of the wave-vector field. The relative importance of wave-number variations, roll curvature, defects, and sidewalls was determined, with the Swift-Hohenberg model as a framework for analysis. Deviations from the model become pronounced for $\frac{(R\ensuremath{-}{R}_{c})}{{R}_{c}}>2$, where ${R}_{c}$ is the critical Rayleigh number.