Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State
arXiv:chao-dyn/9808006 · doi:10.1103/PhysRevE.58.R6903
Abstract
By analyzing large-aspect-ratio spiral-defect-chaos (SDC) convection images, we show that the Karhunen-Loève decomposition (KLD) scales extensively for subsystem-sizes larger than 4d (d is the fluid depth), which strongly suggests that SDC is extensively chaotic. From this extensive scaling, the intensive length ξ_KLD is computed and found to have a different dependence on the Rayleigh number than the two-point correlation length ξ_2. Local computations of ξ_KLD reveal a substantial spatial nonuniformity of SDC that extends over radii 18d< r < 45d in a Γ=109 aspect-ratio cell.
arXiv comment10 pages single-spaced (total), 3 figues, 2 tables
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