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

By analyzing large-aspect-ratio spiral-defect chaos (SDC) convection images , we show that the Karhunen-Loeve decomposition (KLD) scales extensively fo r subsystem sizes larger than 4d (d is the fluid depth), which strongly sug gests that SDC is extensively chaotic. From this extensive scaling, the int ensive 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 c omputations of xi(KLD) reveal a spatial nonuniformity of SDC images that ex tends over radii 18d<r<45d in a Gamma=109 aspect-ratio cell. [S1063-651X(98 )50412-6].