Starting with a swirling flow we prove the existence of unique turbulent solutions of the stochastically driven Navier-Stokes equation in three dimensions. These solutions are not smooth but Hölder continuous with index 1/3. The turbulent solutions give the existence of an invariant measure that determines the statistical theory of turbulence including Kolmogorov´s scaling laws. We will discuss how the invariant measure can be approximated leading to a implicit formula that can be used to compare with simulations and experiments.