# Séminaire de Mécanique d'Orsay

## Le Jeudi 17 juin 2021 à 14h00 - Webinaire - le lien sera communiqué ultérieurement

### Turbulence in real situations: the case of Poiseuille flows

## Yves Pomeau

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This is a work done with Martine Le Berre on one of the most simple real turbulent flow: the plane Poiseuille flow between two parallel planes driven by a pressure gradient parallel to those planes in the limit of a very large pressure gradient. The theoretical understanding of wall bounded flows like this one,commonly refers to the log-law of von-Karman-Prandtl law valid close to the walls. This law relies on the introduction of the Prandtl length which is itself extrapolated from Boussinesq theory of turbulence. I shall explain how a rational theory of turbulence (inhomogeneous and anisotropic) can be built. Applied to Poiseuille flows, this covers both the neighborhood of the wall, and the rest of the channel. Because of the simplicity of the geometry this can be formulated in a rather simple way and the corresponding equations can be solved almost explicitly in the limit of a large Reynolds number, with different approximations in different domains that are matched near the boundaries. This yields in particular a concrete form of the velocity profile with very thin boundary layers near the walls. At very large Reynolds number, Re, the flow is made of a plug flow of relative amplitude growing like log(Re), plus a tent-like flow with a maximum, of complex inner structure, near the middle of the channel, plus two thin boundary layers at the walls. If time permits I'll draw some conclusions from this analysis for the general case of the turbulent friction.

Accès Webinaire - le lien sera communiqué ultérieurement