Journal of Fluid Mechanics


Relationship between temporal and spatial averages in grid turbulence

L. Djenidia1 c1, S. F. Tardua2 and R. A. Antoniaa1

a1 Discipline of Mechanical Engineering, School of Engineering, University of Newcastle, Newcastle, 2308 NSW, Australia

a2 Laboratoires des Ecoulements Geophysiques et Industriels, LEGI BP 53 X Grenoble, France


A long-time direct numerical simulation (DNS) based on the lattice Boltzmann method is carried out for 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 DNS of grid turbulence, since it justifies the use of spatial averaging along a lateral direction and over several realizations for determining 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 along lateral directions, the equality between the two types of averaging provides strong support for the ergodic hypothesis in grid turbulence in planes perpendicular to the mean flow.

(Received October 22 2012)

(Revised May 28 2013)

(Accepted July 08 2013)

(Online publication August 02 2013)

Key words

  • homogeneous;
  • isotropic turbulence


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