## ON THE ERGODICITY OF GRID TURBULENCE
## RésuméA long time running direct numerical simulation (DNS) based on the lattice Boltzmann method is carried out in grid turbulence with the view to compare spatially averaged statistical properties in planes perpendicular to the mean flow with their temporal counterparts. The results show that the two averages become equal a short distance downstream of the grid. This equality indicates that the flow has become homogeneous in a plane perpendicular to the mean flow. This is an important result, since it confirms that hot-wire measurements are appropriate for testing theoretical results based on spatially averaged statistics. It is equally important in the context of DNSs of grid turbulence, since it justifies the (lateral) spatial averaging using several realizations, to determine various statistical properties. Finally, the very good agreement between temporal and spatial averages validates the comparison between temporal (experiments) and spatial (DNS) statistical properties. |

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