Constant flux relation for driven dissipative systems

TL;DR

This paper introduces a universal scaling law for flux correlation functions in driven dissipative systems, generalizing classical turbulence laws and deriving new exact relations for particle aggregation and wave turbulence models.

Contribution

It presents a novel universal flux relation applicable across various driven dissipative systems, extending classical turbulence laws and deriving new exact scaling relations.

Findings

Derived a universal flux relation for dissipative systems

Established new exact scaling laws for particle aggregation models

Extended the 4/5 law to wave turbulence scenarios

Abstract

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 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.