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

TL;DR

This study investigates how mean flow influences spiral defect chaos in generalized Swift-Hohenberg models, revealing a transition from slow coarsening to spatiotemporal chaos as mean flow strength increases.

Contribution

It introduces a detailed analysis of mean flow effects on pattern dynamics in Swift-Hohenberg models, highlighting the transition to chaos with varying mean flow strength.

Findings

Weak mean flow leads to slow coarsening and large target defects.

Strong mean flow induces spatiotemporal chaos with positive Lyapunov exponent.

Differences in mean flow spatial features compared to Rayleigh-Bénard convection are quantified.

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.