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ISSN オンライン: 2642-0554

ON THE ERGODICITY OF GRID TURBULENCE

Lyazid Djenidi
Discipline of Mechanical Engineering, University of Newcastle, Newcastle, 2308, NSW, AUSTRALIA

Sedat Tardu
Laboratoire des Ecoulements Geophysiques et Industriels (LEGI) UMR 5519/Universite de Grenoble 38402 Saint mrtin d'heres Cedex France

Robert Anthony Antonia
Discipline of Mechanical Engineering, University of Newcastle, Newcastle, 2308, NSW, AUSTRALIA

要約

A 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.
The results are also interesting because, since the flow is stationary in time and spatially homogeneous in the lateral directions, the equality between the two types of averaging can be seen to provide support for the ergodic hypothesis in grid turbulence in planes perpendicular to the mean flow.