Exploring Spiral Defect Chaos in Generalized Swift-Hohenberg Models with Mean Flow

Abstract

We explore the phenomenon of spiral defect chaos in two types of generalized Swift-Hohenberg model equations that include the effects of long-range drift velocity or mean flow. We use spatially-extended domains and integrate the equations for very long times to study the pattern dynamics as the magnitude of the mean flow is varied. The magnitude of the mean flow is adjusted via a real and continuous parameter that accounts for the fluid boundary conditions on the horizontal surfaces in a convecting layer. For weak values of the mean flow we find that the patterns exhibit a slow coarsening to a state dominated by large and very slowly moving target defects. For strong enough mean flow we identify the existence of spatiotemporal chaos which is indicated by a positive leading order Lyapunov exponent. We compare the spatial features of the mean flow field with that of Rayleigh-B\'enard convection and quantify their differences in the neighborhood of spiral defects.