Just to make you aware of a couple of preprints, that appeared late last year, proving for the first time some dynamical behaviour observed in turbulence in the context of stochastic Navier-Stokes equations, see this featured article in Quantamagazine. Adding noise helps mastering this problem, but in addition I would like to emphasize the importance of the dynamical systems approach in proving the desired phenomena; in particular, ergodicity (of the one-point motion) is not enough.
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