Spiral-pattern formation in Rayleigh-Bénard convection

We present a numerical study of the spontaneous formation of spiral patterns in Rayleigh-Bénard convection in non-Boussinesq fluids. We solve a generalized two-dimensional Swift-Hohenberg equation that includes a quadratic nonlinearity and coupling to mean flow. We show that this model predicts in quantitative detail many of the features observed experimentally in studies of Rayleigh-Bénard convection in ${\mathrm{CO}}_2$ gas. In particular, we study the appearance and stability of a rotating spiral state obtained during the transition from an ordered hexagonal state to a roll state.