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We use the 2 particle irreducible Schwinger-Keldysh effective action to setup consistent equations for the velocity and pressure correlations of aturbulent flow. We use these equations to derive the Kadanoff-Baym equationsdescribing the relaxation to Kolmogorov turbulence in the absence of meanvelocities.

Kadanoff-Baym equations for near-Kolmogorov turbulence