The state-space structure around spiral defect chaos in
Rayleigh-Bénard convection
Rayleigh-Bénard convection
File(s)
Published version
Author(s)
Chan, Chi Hin
Hossain, Mohammad
Sherwin, Spencer
Hwang, Yongyun
Type
Journal Article
Abstract
The co-existence of ideal straight rolls (ISRs) and
spiral-defect chaos (SDC) as bistable states in Rayleigh-Bénard convection 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 localised structures of SDC by gradually reducing the spatial domain. By minimising the domain
systematically to Γ = 4π, SDC appears transiently and
eventually stabilises 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 further 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.
spiral-defect chaos (SDC) as bistable states in Rayleigh-Bénard convection 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 localised structures of SDC by gradually reducing the spatial domain. By minimising the domain
systematically to Γ = 4π, SDC appears transiently and
eventually stabilises 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 further 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.
Date Issued
2026-02-01
Date Acceptance
2025-11-17
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2026, 482 (2332)
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
482
Issue
2332
Copyright Statement
© 2026 The Authors. Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
License URL
Identifier
10.1098/rspa.2024.0974
Subjects
convection
instabilities
transition
Publication Status
Published
Article Number
20240974
Date Publish Online
2026-02-18