Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State
Scott M. Zoldi, Jun Liu, Kapil M. S. Bajaj, Henry S. Greenside, Guenter Ahlers
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 ξKLD is computed and found to have a different dependence on the Rayleigh number than the two-point correlation length ξ2. Local computations of ξKLD reveal a substantial spatial nonuniformity of SDC that extends over radii 18d< r < 45d in a Γ=109 aspect-ratio cell.
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