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    Ting, David S-K. 2016. Basics of Engineering Turbulence.

    Laizet, S. Nedić, J. and Vassilicos, J. C. 2015. The spatial origin of −5/3 spectra in grid-generated turbulence. Physics of Fluids, Vol. 27, Issue. 6, p. 065115.

    Djenidi, L. Tardu, S.F. Antonia, R.A. and Danaila, L. 2014. Breakdown of Kolmogorov's first similarity hypothesis in grid turbulence. Journal of Turbulence, Vol. 15, Issue. 9, p. 596.

    Djenidi, L. and Antonia, R. A. 2014. Transport equation for the mean turbulent energy dissipation rate in low- grid turbulence. Journal of Fluid Mechanics, Vol. 747, p. 288.

    Lefeuvre, N. Thiesset, F. Djenidi, L. and Antonia, R. A. 2014. Statistics of the turbulent kinetic energy dissipation rate and its surrogates in a square cylinder wake flow. Physics of Fluids, Vol. 26, Issue. 9, p. 095104.

  • Journal of Fluid Mechanics, Volume 730
  • September 2013, pp. 593-606

Relationship between temporal and spatial averages in grid turbulence

  • L. Djenidi (a1), S. F. Tardu (a2) and R. A. Antonia (a1)
  • DOI:
  • Published online: 02 August 2013

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.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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