LEGI - UMR 5519

Financement : ED de physique

Collaboration : V. Rossetto et L. Canet (LPMMC, Grenoble)

The first statistical description of turbulence was proposed by Kolmogorov in 1941. It is based on the assumption of energy cascade and self-similarity and gives predictions for some statistical quantities; however, systematic deviations from this model are observed. Theoretical explanation of the Kolmogorov’s scaling laws and its deviations on the basis of Navier-Stokes equation remains an unsolved problem. Recently, a new theoretical approach to the statistical study of turbulence was proposed: the non-perturbative (or functional) renormalization group (NPRG) method. The departing point of this approach is the forced Navier-Stokes equation of incompressible flow. It leads to a statistical description of turbulent flow in terms of multipoint spatio-temporal correlation functions.

This work aims to compare the new theoretical predictions of the statistical quantities for 3D homogeneous isotropic turbulence with the numerical simulations. For this purpose, a set of high resolution direct numerical simulations (DNS) of a 3D turbulent flows is performed with the use of SCALES code developed in the team MOST. It represents a parallel code implementing a pseudospectral solver of the incompressible Navier-Stokes equation. The simulations were performed for turbulent flow in a cubic domain with periodic boundary conditions under random forcing, in order to enable comparison with the theoretical model of the homogeneous isotropic turbulence.
The first part of the work is dedicated to the study of the near-dissipative range in the energy spectrum. The analysis of the data resulting from DNS shows that the shape of the energy spectrum approaches the theoretically predicted one with the increase in Reynolds number and also allows estimating the near-dissipative range of wavenumbers. These estimations were used for the treatment of the experimental data from the grid turbulence. The experimental data also appears to be in a good agreement with the NPRG theory.

The second part of the work aims to test the theoretical result for the two-point spatio-temporal correlations functions. It showed that the correlations must decay in time as a gaussian function at small time lags and a so-called ‘sweeping’ time scale must arise. The numerical data confirms this prediction. There is also a work in progress on the study of the two-point correlation functions at large time lags.

The further work will focus on the numerical computation of the three-point spatio-temporal correlation functions and comparison with the theoretical results.

Publications

Peer-reviewed Publications

2021

Gorbunova, A., Balarac, G., Canet, L., Eyink, G., & Rossetto, V. (2021). Spatio-temporal correlations in three-dimensional homogeneous and isotropic turbulence. Physics of Fluids, 33(4), 045114.

  

Gorbunova, A., Pagani, C., Balarac, G., Canet, L., & Rossetto, V. (2021). Eulerian spatiotemporal correlations in passive scalar turbulence. Physical Review Fluids, 6(12), 124606.

  

2020

Gorbunova, A., Balarac, G., Bourgoin, M., Canet, L., Mordant, N., & Rossetto, V. (2020). Analysis of the dissipative range of the energy spectrum in grid turbulence and in direct numerical simulations. Physical Review Fluids, 5(4).

  

2017

Canet, L., Rossetto, V., Wschebor, N., & Balarac, G. (2017). Spatiotemporal velocity-velocity correlation function in fully developed turbulence. Physical Review E, 95, 023107.