Spatiotemporal chaos in a model of Rayleigh-Bénard convection

We present a numerical investigation of mean-flow induced spiral turbulence in a generalized Swift-Hohenberg model in two dimensions. We show the existence of a spatiotemporal chaotic state comprised of a large number of rotating spirals in a large aspect ratio system. This state is not predicted by classical theory. We calculate the spatial correlation functions for the order parameter, vorticity, and mean flow field in order to characterize more quantitatively the spiral chaos state. Our simulations show that there is a power-law behavior in the temporal dynamics of spiral defect chaos. Our study suggests that this spiral defect state occurs for low Prandtl numbers and large aspect ratios. We use as global variables the spectra entropy and the magnitude of the vorticity to characterize the transition from the global parallel roll state to the localized spiral state. Unfortunately we cannot determine whether this transition is gradual or sharp.