  This paper is concerned with Kolmogorov's two-equation model for the free
turbulence in three dimensions. We first discuss scaling laws for slightly more
general two-equation models to highlight the special role of the model devised
by Kolmogorov in 1942. The main part of the paper consists in proving the
existence of weak solutions of Kolmogorov's under space-periodic boundary
conditions in a cube. To this end, we provide new a priori estimates and invoke
existence result for pseudo-monotone operators.
