Invariant states in inclined layer convection. Part 1. Temporal transitions along dynamical connections between invariant states. (10th September 2020)

• Record Type: Journal Article
• Authors: Reetz, Florian; Schneider, Tobias M.
• Is Part Of: Journal of fluid mechanics. Volume 898(2020)
• Publication Date: 2020-09-10
• Subjects: pattern formation, -- nonlinear instability; Fluid mechanics -- Periodicals; 532.005
• DOI: 10.1017/jfm.2020.317
• Languages: English
• ISSNs: 0022-1120

Abstract

Abstract : Abstract : Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number $\mathit{Pr}=1.07$ . Depending on the angle of inclination and the imposed temperature difference, the flow exhibits a large variety of self-organized spatio-temporal convection patterns. Close to onset, these patterns have been explained in terms of linear stability analysis of primary and secondary flow states. At a larger temperature difference, far beyond onset, experiments and simulations show complex, dynamically evolving patterns that are not described by stability analysis and remain to be explained. Here we employ a dynamical systems approach. We construct stable and unstable exact invariant states, including equilibria and periodic orbits of the fully nonlinear three-dimensional Oberbeck–Boussinesq equations. These invariant states underlie the observed convection patterns beyond their onset. We identify state space trajectories that, starting from the unstable laminar flow, follow a sequence of dynamical connections between unstable invariant states until the dynamics approaches a stable attractor. Together, the network of dynamically connected invariant states mediates temporal transitions between coexisting invariant states and thereby supports the observed complex time-dependent dynamics in inclined layer convection.