# Some Aspects of Turbulence in Discrete Mechanics

## Quelques aspects de la turbulence en mécanique discrète (anglais)

Jean-Paul Caltagirone
Université de Bordeaux

Stéphane Vincent
Université Paris-Est Marne-La-Vallée

Published on 5 February 2019   DOI : 10.21494/ISTE.OP.2019.0328

### Mots-clés

The discrete mechanics formalism and equations are considered in the present work in order to establish the role played by representative motion equations on the study of turbulence in fluids. In particular, a set of differences related to the turbulent pressure, the dynamics of vorticity in two spatial dimensions, the turbulent dissipation or the divergence of acceleration are discussed compared to the classical continuous media and Navier-Stokes equations. A second part is devoted to presenting on a first example, the rigid rotational motion, the differences between discrete and continuum mechanics. A last section is devoted to simulating the turbulent channel flow at turbulent Reynolds number of Reτ = 590. It is demonstrated that discrete mechanics allow to recover accurately the mean velocity profiles of reference DNS and also to provide scale laws of the whole mean velocity profile from the wall to the center of the channel.

The discrete mechanics formalism and equations are considered in the present work in order to establish the role played by representative motion equations on the study of turbulence in fluids. In particular, a set of differences related to the turbulent pressure, the dynamics of vorticity in two spatial dimensions, the turbulent dissipation or the divergence of acceleration are discussed compared to the classical continuous media and Navier-Stokes equations. A second part is devoted to presenting on a first example, the rigid rotational motion, the differences between discrete and continuum mechanics. A last section is devoted to simulating the turbulent channel flow at turbulent Reynolds number of Reτ = 590. It is demonstrated that discrete mechanics allow to recover accurately the mean velocity profiles of reference DNS and also to provide scale laws of the whole mean velocity profile from the wall to the center of the channel.