Conservation laws constrain the stationary state statistics of driven dissipative systems because the average flux of a conserved quantity between driving and dissipation scales should be constant. This requirement leads to a universal scaling law for flux-measuring correlation functions, which generalizes the $\frac{4}{5}$th law of Navier-Stokes turbulence. We demonstrate the utility of this simple idea by deriving new exact scaling relations for models of aggregating particle systems in the fluctuation-dominated regime and for energy and wave action cascades in models of strong wave turbulence.

• Received 4 August 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.080601