Impact of the variations of the mixing length in a first order turbulent closure system

Abstract

This paper is devoted to the study of a turbulent circulation model. Equations are derived from the “Navier-Stokes turbulent kinetic energy” system. Some simplifications are performed but attention is focused on non linearities linked to turbulent eddy viscosity . The mixing length acts as a parameter which controls the turbulent part in . The main theoretical results that we have obtained concern the uniqueness of the solution for bounded eddy viscosities and small values of and its asymptotic decreasing as in more general cases. Numerical experiments illustrate but also allow to extend these theoretical results: uniqueness is proved only for small enough while regular solutions are numerically obtained for any values of . A convergence theorem is proved for turbulent kinetic energy: as but for velocity we obtain only weaker results. Numerical results allow to conjecture that and as So we can conjecture that this classical turbulent model obtained with one degree of closure regularizes the solution.