Extensive Scaling and Nonuniformity of the Karhunen-Lo\`eve Decomposition for the Spiral-Defect Chaos State
Abstract
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 KLD is computed and found to have a different dependence on the Rayleigh number than the two-point correlation length 2. Local computations of KLD reveal a substantial spatial nonuniformity of SDC that extends over radii 18d< r < 45d in a =109 aspect-ratio cell.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.