Characterization of the Transition from Defect to Phase Turbulence

For the complex Ginzburg-Landau equation on a large periodic interval, we show that the transition from defect to phase turbulence is more accurately described as a smooth crossover rather than as a sharp continuous transition. We obtain this conclusion by using a parallel computer to calculate various order parameters, especially the density of space-time defects, the Lyapunov dimension density, and correlation lengths. Remarkably, the correlation length of the field amplitude fluctuations is, within a constant factor, equal to the length scale defined by the dimension density.