Dynamics of convection

Abstract

Thermal convection in a fluid layer is an example of a dynamical system governed by partial differential equations. As the relevant control parameter (the Rayleigh number) is increased, successive bifurcations may lead to chaos and the nature of the transition depends on the spatial structure of the flow. Numerical experiments with idealized symmetry and boundary conditions make it possible to explore nonlinear behaviour in some detail and to relate bifurcation structures to those found in appropriate low-order systems. Two examples are used to illustrate transitions to chaos. In two-dimensional thermosolutal convection, where the spatial structure is essentially trivial, chaos is caused by a heteroclinic bifurcation involving a symmetric pair of saddle foci. When convection is driven by internal heating several competing spatial structures are involved and the transition to chaos is more complicated in both two- and three-dimensional configurations. Although the first few bifurcations can be isolated a statistical treatment is needed for behaviour at high Rayleigh numbers.