Our paper about mean-flow/turbulence interaction in the context of the 2D vortex condensate has just been published in Physical Review Letters. In this paper, we provide explicit formulae for the Reynolds stress tensor in the inertial limit, and test those formulae againt Direct Numerical Simulations.
Read more about it in this post
Turbulence statistics in a 2D vortex condensate
Anna Frishman, Corentin Herbert Phys. Rev. Lett. 120:204505, 2018