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

TL;DR

This paper proves the existence of global weak solutions for Kolmogorov's two-equation turbulence model in three dimensions and discusses its scaling laws, highlighting its unique role in turbulence modeling.

Contribution

It establishes the existence of weak solutions for Kolmogorov's model using new a priori estimates and pseudo-monotone operator theory, and analyzes its scaling laws.

Findings

Existence of weak solutions under periodic boundary conditions

New a priori estimates for the model

Insights into the model's scaling laws

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.