Geometric evolution of the Reynolds stress tensor in three-dimensional turbulence

Sergey L. Gavrilyuk (1, 2) , Henri Gouin (3)

1 IUSTI - Institut universitaire des systèmes thermiques industriels
2 SMASH - Simulation, modeling and analysis of heterogeneous systems
3 M2P2 - Modélisation et Simulation Numérique (en mécanique des fluides)

The dynamics of the Reynolds stress tensor is determined by an evolution equation coupling geometrical effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are neglected. Then, the Reynolds stress tensor is expressed as the sum of three tensor products of vector fields, which are governed by a distorted gyroscopic equation. Along the mean flow trajectories and in the directions of the vector fields, the fluctuations of velocity are determined by differential equations whose coefficients depend only on the mean flow deformation.

Mots clés: Reynolds stress tensor; Turbulent flows; Gyroscopic equation

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

Sergey L. Gavrilyuk, Henri Gouin. Geometric evolution of the Reynolds stress tensor in three-dimensional turbulence. Geometric Evolution of the Reynolds Stress Tensor in Three-Dimensional Turbulence, Jun 2009, Palermo, Italy. pp.182-191. ⟨hal-00371444v2⟩