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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
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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.

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Scott M. Zoldi, Jun Liu, Kapil M. S. Bajaj, Henry S. Greenside, Guenter Ahlers. 1998-08-05. Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State. https://doi.org/10.1103/physreve.58.r6903

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