Quantum Solution of Classical Turbulence

Using the loop equation, we reduce the problem of decaying turbulence in the $3 + 1$ dimensional Navier–Stokes equation to the quantum mechanics of $N$ Fermi particles on a ring in one dimension, interacting with an Euler ensemble of random fractions $p/q$ with denominator $q < N$.
We find the solution of this system in the statistical limit $N \to \infty$ and compute the energy spectrum, dissipation rate, and velocity correlation function in decaying turbulence without approximations and fitted parameters. We find the whole spectrum of critical indexes, some of which are real, but others are complex numbers related to zeros of the Riemann $\zeta$ function.
Grid turbulence experimental data and the recent large-scale DNS verify our predictions for the energy decay curve and the energy spectrum. All scaling laws — K41, multifractal and Heisenberg — are ruled out.