Bifurcation Sequences in Problems of Thermal Convection and of Plane Couette Flow

Abstract

Rayleigh-Bénard convection in a fluid layer heated from below represents the simplest system with the highest degree of symmetry in which the transition to complex states of fluid flow can be investigated. Through the process of subsequent bifurcations new degrees of freedom are occupied and new mechanisms of heat, mass and momentum transport are introduced as the control parameter is increased. Various bifurcation sequences can be followed depending primarily on the Prandtl number of the fluid. They all start with convection in the form of rolls since we shall assume symmetry of the material properties and the boundaries about the midplane of the layer. The bifurcations lead either to knot convection, oscillatory knot convection and asymmetric knot oscillations (Clever and Busse 1989a), or to bimodal convection, oscillating bimodal convection and spoke pattern convection (Busse 1967, Frick, Busse and Clever 1983, Clever and Busse 1994), or to travelling wave convection and asymmetric travelling wave convection (Clever and Busse 1987, 1989b). Comparisons with experimental observations are possible in several cases. The mechanisms introduced by the bifurcations can be characterized by certain broken symmetries and are relatively independent of the sequence in which the bifurcations occur. The processes of thermal plume formation, eruption of thermal blobs from the boundary layers, and mean flow generation which are observed as coherent