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Defect--Defect Correlation Functions, Generic Scale Invariance, and the Complex Ginzburg--Landau Equation

Motivated by the idea of developing a ``hydrodynamic'' description of spatiotemporal chaos, we have investigated the defect--defect correlation functions in the defect turbulence regime of the two--dimensional, anisotropic complex Ginzburg--Landau equation. We compare our results with the predictions of generic scale invariance. Using the topological nature of the defects, we prove that defect--defect correlations cannot decay as slowly as predicted by generic scale invariance. We also present results on the fluctuations of the amplitude field $A$.