Simulating Complex Dynamics In Intermediate And Large-Aspect-Ratio Convection Systems

Buoyancy-induced (Rayleigh-Bénard) convection of a fluid between two horizontal plates is a central paradigm for studying the transition to complex spatiotemporal dynamics in sustained nonequilibrium systems. To improve the analysis of experimental data and the quantitative comparison of theory with experiment, we have developed a three-dimensional finite-difference code that can integrate the three-dimensional Boussinesq equations (which govern the evolution of the temperature, velocity, and pressure fields associated with a convecting flow) efficiently in large box-shaped domains with experimentally appropriate lateral boundary conditions. We discuss some details of this code and present two applications, one to the occurrence of quasiperiodic dynamics with as many as 5 incommensurate frequencies in a moderate-aspect-ratio 10× 5 convection cell, and one to the onset of spiral defect chaos in square cells with aspect ratios varying from Γ = 16 to 56.