The Kolmogorov Law of turbulence, What can rigorously be proved ? Part II

Roger Lewandowski (1) , Benoît Pinier (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We recall what are the different known solutions for the incompressible Navier-Stokes Equations, in order to fix a suitable functional setting for the probabilistic frame that we use to derive turbulence models, in particular to define the mean velocity and pressure fields, the Reynolds stress and eddy viscosities. Homogeneity and isotropy are discussed within this framework and we give a mathematical proof of the famous −5/3 Kolmogorov law, which is discussed in a numerical simulation performed in a numerical box with a non trivial topography on the ground.

Mots clés: Navier Stokes Equations; Turbulence models

Domaines: Physique mathématique [math-ph]; Mécanique des fluides [physics.class-ph]

Roger Lewandowski, Benoît Pinier. The Kolmogorov Law of turbulence, What can rigorously be proved ? Part II. The Foundations of chaos revisited: from Poincaré to recent advancements, Springer, pp.71-89, 2016, 978-3-319-29699-9. ⟨10.1007/978-3-319-29701-9_5⟩. ⟨hal-01244651⟩