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Are there any references to the derivation of the Kolmogorov-Obukhov theory for fully developed turbulent flow in 2-dimensions? That is, the derivation of the Kolmogorov power rules, but in 2D? I was only able to find results but not actual, rigorous derivations/proofs.

Thanks!

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The theory of two-dimensional turbulence was developed by Kraichnan so maybe you want to check out his paper on 2D-inertial ranges, "Inertial Ranges in Two-Dimensional Turbulence" R. Kraichnan, 1967.

I would also recommend a recent review on turbulent cascades: "Cascades and transitions in turbulent flows" by Alexakis and Biferale (2018)

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