On the state space structure of spiral-defect chaos in Rayleigh-Bénard convection

The existence of bistability between ideal straight rolls (ISRs) and spiral-defect chaos (SDC) in Rayleigh-Bénard convection is well established. Extensive SDC have been observed in large domains, characterised by localised structures of a specific length scale. This study aims to isolate these structures by systemically reducing the domain size, starting from a large domain. In a moderate domain, a transient chaotic state is observed before transitioning into multiple stationary, travelling-wave and time-periodic states. We identify and label 14 of these states as elementary states of SDC. Subsequently, we investigate the state space structure of the elementary states and explore their connections to SDC and ISRs. In particular, we examine the linear instabilities outside of the boundaries of the Busse balloon and determine their asymptotic behaviours. Near the Busse balloon, the asymptotic states lead to ISRs. As we move further away from the Busse balloon, we identify linear pathways leading to transient chaotic state, ultimately setlling into a travelling-wave state. The state space structure of these linear pathways will be presented in this presentation.