The state-space structure around spiral-defect chaos in Rayleigh–Bénard convection

The co-existence of ideal straight rolls (ISRs) and spiral-defect chaos (SDC) as bistable states in Rayleigh–Bénard convection (RBC) above the onset of the linear instability is well established in extended spatial domains (Γ≥80, where Γ is the aspect ratio of the domain). However, multiple stable states have also been found independently, raising questions about the precise understanding of this observed bistability in extended domains. In this study, we isolate the localized structures of SDC by gradually reducing the spatial domain. By minimizing the domain systematically to Γ=4π, SDC appears transiently and eventually stabilizes into new stable states referred to as elementary states. These elementary states are visibly and statistically similar to the spatially local patterns of SDC, indicative of invariant solutions underpinning the pattern formation in SDC. To understand the state-space structure further, we have examined the edge between ISRs and the elementary states, revealing multiple edge states, and conducted a series of numerical simulations along the unstable manifolds of unstable ISRs. The unstable ISRs near the Busse balloon are connected to stable ISRs and the base state through networks of heteroclinic orbits, forming a basin of attraction for each stable ISR. In contrast, the unstable ISRs farther from the Busse balloon contain some unstable manifolds, along which the solution trajectory leads to SDC, suggesting that these unstable ISRs sit on the boundary between stable ISRs and SDC. Finally, we propose a state-space structure around the basic heat conduction state, stable/unstable ISRs, elementary states and transient SDC.