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

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 ( $\gamma$ ) and Rayleigh number ( $\textit{Ra}$ ), a variety of spatio-temporal patterns is observed. We investigate the switching diamond panes (SDP) pattern, observed at $(\gamma , \textit{Ra})\simeq (100^\circ ,10\,000)$ , which exhibits large-scale oblique features and is one of the five complex tertiary patterns at Prandtl number $\textit{Pr}=1.07$ . 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 large-scale structure and small-scale defects of modulated rolls. Parametric continuation in $\textit{Ra}$ 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.