On the existence of global-in-time weak solutions and scaling laws for Kolmogorov's two-equation model of turbulence

Abstract

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.

arXiv commentIn the third version the notion of weak solution is improved; and a proposition is added which shows that smooth weak solutions are classical solutions. The fourth version contains an improvement on the argument involving Steklov averages in Section 3