Direct numerical simulations of transitional Rayleigh–Bénard Poiseuille flows

We investigate the transitional flow regimes arising from the interaction between buoyancy and shear in Rayleigh–Bénard–Poiseuille (RBP) flows, considering both large and small domains. The transition boundaries between the bistable system consisting of spiral defect chaos (SDC) and ideal straight rolls (ISRs) in Rayleigh–Bénard convection, and subcritical turbulence in plane Poiseuille flows are not known. Using direct numerical simulations in a large spatial domain over a range of Rayleigh numbers, $Ra \in [0, 10000]$ , Reynolds numbers, $\textit{Re} \in [0, 2000]$ and unit Prandtl number, we identify five distinct regimes: (i) bistable SDC and ISRs; (ii) ISRs; (iii) wavy rolls; (iv) intermittent rolls; and (v) shear-driven turbulence. The newly identified intermittent rolls state features longitudinal rolls that decay towards the laminar state before regenerating. In the turbulent regime, longitudinal rolls may coexist with turbulent–laminar bands, highlighting the role of longitudinal rolls in transitional RBP flows. To this end, we examine the unstable manifold of longitudinal rolls in a small domain, integrating along which led to turbulence. This turbulence occur transiently, decaying towards the unstable laminar base state where the longitudinal rolls can be excited again, forming a quasi-cyclic process referred to as the thermally assisted sustaining process (TASP). We further investigate the behaviour of TASP as $\textit{Re}$ and $Ra$ are varied, revealing a stable periodic orbit around the longitudinal roll and the laminar state, and a pathway towards turbulence above a certain $\textit{Re}$ threshold. Finally, we provide a state space sketch of the dynamical processes, emphasising the role of longitudinal rolls in transitional RBP in small domains, and discuss the potential connections to large domains.