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Local and global bifurcations to large-scale oblique patterns in inclined layer convection.

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Title: Local and global bifurcations to large-scale oblique patterns in inclined layer convection.
Authors: Zheng, Zheng1, Azimi, Sajjad1,2, Reetz, Florian1, Schneider, Tobias M.1 tobias.schneider@epfl.ch
Source: Journal of Fluid Mechanics. 5/25/2026, Vol. 1035, p1-28. 28p.
Abstract: In the inclined layer convection system, thermal convection in a Rayleigh-Bénard cell tilted against gravity, the flow is subject to competing buoyancy and shear forces. For varying inclination angle (γ) and Rayleigh number (Ra), a variety of spatio-temporal patterns is observed. We investigate the switching diamond panes (SDP) pattern, observed at (γ, Ra(100®, 10 000), which exhibits large-scale oblique features and is one of the five complex tertiary patterns at Prandtl number Pr=1.07. First, we study the linear instability of the secondary-state transverse convection rolls and the five branches including two travelling waves and three periodic orbits, bifurcating simultaneously from it. These non-generic bifurcations arise from the breaking of specific spatial symmetries of transverse rolls, and the resulting bifurcated solutions show large-scale diamond-shaped amplitude modulations. Second, we explore a periodic orbit that captures both the largescale structure and small-scale defects of modulated rolls. Parametric continuation in Ra reveals the global homoclinic bifurcation via which this periodic orbit emerges. Third, the edge states between two dynamically relevant periodic orbits have been computed. Specifically, additional steady and time-periodic solutions are identified on the basin boundary and their bifurcation structures are analysed. Together, using nonlinear invariant solutions and their bifurcations, we take a further step toward understanding the emergence and dynamics of SDP far from the onset of convection, where linear methods have not been applied successfully. [ABSTRACT FROM AUTHOR]
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Abstract:In the inclined layer convection system, thermal convection in a Rayleigh-Bénard cell tilted against gravity, the flow is subject to competing buoyancy and shear forces. For varying inclination angle (γ) and Rayleigh number (Ra), a variety of spatio-temporal patterns is observed. We investigate the switching diamond panes (SDP) pattern, observed at (γ, Ra(100®, 10 000), which exhibits large-scale oblique features and is one of the five complex tertiary patterns at Prandtl number Pr=1.07. First, we study the linear instability of the secondary-state transverse convection rolls and the five branches including two travelling waves and three periodic orbits, bifurcating simultaneously from it. These non-generic bifurcations arise from the breaking of specific spatial symmetries of transverse rolls, and the resulting bifurcated solutions show large-scale diamond-shaped amplitude modulations. Second, we explore a periodic orbit that captures both the largescale structure and small-scale defects of modulated rolls. Parametric continuation in Ra reveals the global homoclinic bifurcation via which this periodic orbit emerges. Third, the edge states between two dynamically relevant periodic orbits have been computed. Specifically, additional steady and time-periodic solutions are identified on the basin boundary and their bifurcation structures are analysed. Together, using nonlinear invariant solutions and their bifurcations, we take a further step toward understanding the emergence and dynamics of SDP far from the onset of convection, where linear methods have not been applied successfully. [ABSTRACT FROM AUTHOR]
ISSN:00221120
DOI:10.1017/jfm.2026.11487