Extensive scaling and nonuniformity of the Karhunen-Loève decomposition for the spiral-defect chaos state

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 spatial nonuniformity of SDC images that extends over radii 18d<r<45d in a Γ = 109 aspect-ratio cell.

Duke Scholars

Author Henry Greenside Physics