Abstract
We develop two measures to characterize the geometry of patterns exhibited by the state of spiral defect chaos, a weakly turbulent regime of Rayleigh-Benard convection. These describe the packing of contiguous stripes within the pattern by quantifying their length and nearest-neighbor distributions. The distributions evolve towards a unique distribution with increasing Rayleigh number that suggests power-law scaling for the dynamics in the limit of infinite system size. The techniques are generally applicable to patterns that are reducible to a binary representation.
Highlights
Characterizing the geometry exhibited by a system plays a fundamental role in physics
The convection pattern occurring across the fluid layer was described as the linear instability of the conducting state by Rayleigh [1] and parametrized by a dimensionless number known as the Rayleigh number, R = gαd3ΔT /(νκ)
The extreme confinement of the fluid between the top and bottom plates primarily determines the wave number exhibited by the system
Summary
Characterizing the geometry exhibited by a system plays a fundamental role in physics. At low Prandtl numbers, roll curvature in the horizontal plane can result in long-range pressure gradients that result in mean flows within the system These systems show significantly different patterns from fluids with high Prandtl numbers. The characterizations developed in this paper obtain distributions for the length scales of stripes as well as nearest-neighbor distributions that result from defect dynamics. We reduce the patterns exhibited by the system to a graph This parametrizes the system through the number of nearest-neighbors of each distinct roll. These measures characterize the topology and packing of the striped patterns observed within the convective region and provide unique insights into the underlying dynamics. A similar argument may be made for the number of nearest-neighbors as illustrated in figure 2
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