Extensive Scaling and Nonuniformity of the Karhunen-Lo\`eve   Decomposition for the Spiral-Defect Chaos State
  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. 
Scott M. Zoldi (1), Jun Liu (2), Kapil M. S. Bajaj (3), Henry S.   Greenside (4), and Guenter Ahlers (3) ((1) Theoretical Di...