Spiral defect chaos in a model of Rayleigh-Bénard convection

Abstract

A numerical solution of a generalized Swift-Hohenberg equation in two dimensions reveals the existence of a spatiotemporal chaotic state comprised of a large number of rotating spirals. This state is observed for a reduced Rayleigh number \ensuremath{\epsilon}=0.25. The power spectrum of the state is isotropic, and the spatial correlation function decays exponentially, with an estimated decay length \ensuremath{\xi}\ensuremath{\approxeq}2.5${\ensuremath{\lambda}}_{\mathit{c}}$, where ${\ensuremath{\lambda}}_{\mathit{c}}$ is the critical wavelength near the onset of convection. Our study suggests that this spiral defect state occurs for low Prandtl numbers and large aspect ratios.