Invariant states in inclined layer convection. Part 2. Bifurcations and connections between branches of invariant states

TL;DR

This paper investigates the bifurcations and connections between invariant states in inclined layer convection, revealing a complex bifurcation network that explains the diverse flow patterns observed in experiments and simulations.

Contribution

It provides a detailed bifurcation analysis of invariant states in inclined convection, linking exact solutions to observed flow patterns and their stability.

Findings

Identified bifurcations modifying invariant states

Mapped a network connecting 16 invariant states

Linked bifurcation structures to complex flow dynamics

Abstract

Convection in a layer inclined against gravity is a thermally driven non-equilibrium system, in which both buoyancy and shear forces drive spatio-temporally complex flow. As a function of the strength of thermal driving and the angle of inclination, a multitude of convection patterns is observed in experiments and numerical simulations. Several observed patterns have been linked to exact invariant states of the fully nonlinear 3D Oberbeck-Boussinesq equations. These exact equilibria, traveling waves and periodic orbits reside in state space and, depending on their stability properties, are transiently visited by the dynamics or act as attractors. To explain the dependence of observed convection patterns on control parameters, we study the parameter dependence of the state space structure. Specifically, we identify the bifurcations that modify the existence, stability and connectivity of invariant states. We numerically continue exact invariant states underlying spatially periodic convection patterns at Pr=1.07 under changing control parameters for temperature difference between the walls and inclination angle. The resulting state branches cover various inclinations from horizontal layer convection to vertical layer convection and beyond. The collection of all computed branches represents an extensive bifurcation network connecting 16 different invariant states across control parameter values. Individual bifurcation structures are discussed in detail and related to the observed complex dynamics of individual convection patterns. Together, the bifurcations and associated state branches indicate at what control parameter values which invariant states coexist. This provides a nonlinear framework to explain the multitude of complex flow dynamics arising in inclined layer convection.