Just before his arrival at Cornell, I was watching Eberhard Bodenschatz's spiral defect chaos movie. I became convinced that there should be a hydrodynamic description of the motion, where each defect should be like an atom and the atom density (plus defects minus minus defects) should have a long-wavelength description like gases and liquids. Bruce Roberts, Eberhard and I looked hard at this question: Bruce extracted 1/r^2 predictions from a likely theoretical starting point (Generic Scale Invariance, which begins by writing the most general local equation of motion allowed by symmetry, violating detailed balance ...) and ran extensive simulations of a likely model (the Complex Ginzburg-Landau Equation). We found very little in the way of long-range correlations (they certainly decay faster than 1/r^2). Bruce wouldn't write it up, though, until he had proven a bound (using the topological nature of the defects) that ruled out the predicted scaling.
Statistical Mechanics: Entropy, Order Parameters, and Complexity, now available at Oxford University Press (USA, Europe).