M. R. Paul, K-H. Chiam, M. C. Cross, and P. F. Fischer , "Rayleigh-Benard Convection in Large-Aspect-Ratio Domains," Preprint ANL/MCS-P1144-0404, April 2004. [pdf]
The coarsening and wavenumber selection of striped states growing from random initial conditions are studied in a non-relaxational, spatially extended, and far-from-equilibrium system by performing large-scale numerical simulations of Rayleigh-Bénard convection in a large-aspect-ratio cylindrical domain with experimentally realistic boundaries. We find evidence that various measures of the coarsening dynamics scale in time with different power-law exponents, indicating that multiple length scales are required in describing the time dependent pattern evolution. The translational correlation length scales with time as t0.12, the orientational correlation length scales as t0.54, and the density of defects scale as t-0.45. The final pattern evolves toward the wavenumber where isolated dislocations become motionless, suggesting a possible wavenumber selection mechanism for large-aspect-ratio convection.