Spatiotemporal Chaos in Rayleigh-Bénard Convection

Spatiotemporal chaos, or disorder in space and chaos in time, is studied in direct numerical simulations of Rayleigh-Bénard convection. In particular, the following results pertaining to spiral defect chaos are discussed. First, in the absence of the mean flow, spiral defect chaos is found to collapse to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wave numbers that approach those uniquely selected by focus-type singularities, which, in the absence of the mean flow, lie at the zig zag instability boundary. In addition, mean flow is shown to contribute to the phenomenon of rolls terminating perpendicularly into lateral walls. In the absence of the mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with the Rayleigh number. Second, the transport of passive tracers in the presence of advection by spiral defect chaos is found to be characterized by normal diffusion. The enhancement in the tracer diffusivity follows two regimes. When the molecular diffusivity of the tracer concentration is small, the enhancement is proportional to the Péclet number. When the molecular diffusivity is large, the enhancement is proportional to the square root of the Péclet number. This difference is explained in terms of the dependence of the transport on the local wave numbers. It is found that tracer concentrations with small molecular diffusivity experience enhanced longitudinal diffusion and suppressed lateral diffusion at regions of the flow occupied by defects. Third, perturbations in spiral defect chaos are found to propagate in a localized manner. In particular, they nucleate around the defect structures in the flow. In addition, an oscillatory instability at the spiral core is discovered. Finally, the propav gation in pre-chaotic stripe textures is explained in terms of the diffusion of the phase variable of the stripe state.