New relations for correlation functions in Navier-Stokes turbulence

Understand

We consider the steady-state statistics of turbulence sustained by a large-scale force.

• The Kolmogorov flux relation (4/5-law) is shown to be a particular case of the general relation on the current-density correlation function.
• Using that, we derive an analog of the flux relation for compressible turbulence and a new exact relation for incompressible turbulence.