Spirals, defects, rolls and bands; transitional Rayleigh-Bénard poiseuille flows using spectral/hp element methods
File(s)
Author(s)
Chan, Chi Hin
Type
Thesis
Abstract
The transitional regimes of Rayleigh–Bénard–Poiseuille (RBP) flow and Rayleigh–Bénard convection are investigated using direct numerical simulations and linear stability analysis. RBP flow is a canonical configuration in which buoyancy-driven Rayleigh-Bénard convection (RBC) interacts with shear-driven plane Poiseuille flow (PPF). While the transitional dynamics of each system have been extensively studied independently, the transitional regime in which shear and buoyancy forces interact remains largely unexplored, despite its potential engineering implications.
Direct numerical simulations are performed using Nektar++ over Rayleigh numbers, Ra ∈ [0, 10000], and Reynolds numbers, Re ∈ [0, 2000], at a unit Prandtl number in large computational domains. Five distinct regimes are identified: (1) bistable spiral defect chaos (SDC) and ideal straight rolls (ISRs), (2) ISRs, (3) wavy rolls, (4) intermittent rolls, and (5) shear-driven turbulence. The intermittent-roll regime represents a newly identified state characterised by spatio-temporal breakdown and the regeneration of longitudinal rolls. To elucidate the dynamics of the intermittent-roll regime, unstable manifolds of longitudinal rolls are computed in confined domains. Trajectories evolving along these unstable manifolds lead to turbulence which, depending on Re, may be transient and decay into the linearly unstable laminar base state, before returning to rolls. The linearly unstable laminar state, longitudinal rolls and transient turbulence together form a quasi-cyclic process that sustains turbulence, referred to as the thermally-assisted sustaining process (TASP).
The second part of the thesis investigates the bistability between SDC and ISRs in large-domain RBC. Systematic domain reduction reveals that SDC becomes transient and converges to multiple stable invariant solutions, termed elementary states, resembling spatially-localised SDC structures. Analysis of the unstable manifolds of ISRs shows that certain ISRs act as edge states on basin boundaries between ISRs and SDC, while others form heteroclinic connections with stable ISRs, providing a dynamical-system perspective of the bistable system.
Direct numerical simulations are performed using Nektar++ over Rayleigh numbers, Ra ∈ [0, 10000], and Reynolds numbers, Re ∈ [0, 2000], at a unit Prandtl number in large computational domains. Five distinct regimes are identified: (1) bistable spiral defect chaos (SDC) and ideal straight rolls (ISRs), (2) ISRs, (3) wavy rolls, (4) intermittent rolls, and (5) shear-driven turbulence. The intermittent-roll regime represents a newly identified state characterised by spatio-temporal breakdown and the regeneration of longitudinal rolls. To elucidate the dynamics of the intermittent-roll regime, unstable manifolds of longitudinal rolls are computed in confined domains. Trajectories evolving along these unstable manifolds lead to turbulence which, depending on Re, may be transient and decay into the linearly unstable laminar base state, before returning to rolls. The linearly unstable laminar state, longitudinal rolls and transient turbulence together form a quasi-cyclic process that sustains turbulence, referred to as the thermally-assisted sustaining process (TASP).
The second part of the thesis investigates the bistability between SDC and ISRs in large-domain RBC. Systematic domain reduction reveals that SDC becomes transient and converges to multiple stable invariant solutions, termed elementary states, resembling spatially-localised SDC structures. Analysis of the unstable manifolds of ISRs shows that certain ISRs act as edge states on basin boundaries between ISRs and SDC, while others form heteroclinic connections with stable ISRs, providing a dynamical-system perspective of the bistable system.
Version
Open Access
Date Issued
2025-11-05
Date Awarded
2026-03-01
Copyright Statement
Attribution-NonCommercial 4.0 International Licence (CC BY-NC)
License URL
Advisor
Sherwin, Spencer
Hwang, Yongyun
Publisher Department
Department of Aeronautics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)