Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2004-03-08
Nonlinear Sciences
Pattern Formation and Solitons
5 pages, 6 figures
Scientific paper
10.1103/PhysRevLett.93.064503
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-B\'{e}nard 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 $t^{0.12}$, the orientational correlation length scales as $t^{0.54}$, 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.
Chiam K.-H.
Cross M. C.
Fischer Paul F.
Paul Mark R.
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