Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State

Details Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State Extensive Scaling and Nonuniformity of the Karhunen-Loève Decomposition for the Spiral-Defect Chaos State

1998-08-05

arxiv.org/abs/chao-dyn/9808006v1

Nonlinear Sciences

Chaotic Dynamics

10 pages single-spaced (total), 3 figues, 2 tables

Scientific paper

10.1103/PhysRevE.58.R6903

By analyzing large-aspect-ratio spiral-defect-chaos (SDC) convection images, we show that the Karhunen-Lo\`eve 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 \xi_KLD is computed and found to have a different dependence on the Rayleigh number than the two-point correlation length \xi_2. Local computations of \xi_KLD reveal a substantial spatial nonuniformity of SDC that extends over radii 18d< r < 45d in a \Gamma=109 aspect-ratio cell.

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