The organization of near-wall turbulence: a comparison between boundary layer SPIV data and channel flow DNS data

Abstract

The vortical structures of near-wall turbulence at moderate Reynolds number are analyzed and compared in datasets obtained from stereoscopic particle image velocimetry (SPIV) in a turbulent boundary layer and from direct numerical simulations (DNS) in a turbulent channel flow. The SPIV data are acquired in the LTRAC water tunnel at Re _τ=δ⁺=820 in a streamwise/wall-normal plane, and in the LML wind tunnel at Re _τ=δ⁺=2590 in a streamwise/wall-normal plane and in a plane orthogonal to the mean flow. The DNS data is taken from DelAlamo et al. (Self-similar vortex clusters in the turbulent logarithmic region, J. Fluid Mech. 561 (2006), pp. 329–358), at Re _τ=950. The SPIV database is validated through an analysis of its mean velocity profile and power spectra, which are compared with reference profiles. A common detection algorithm is then applied to both the SPIV and DNS datasets in order to retrieve the streamwise and spanwise vortices. The algorithm employed is based on the 2D swirling strength and on a fit of an Oseen vortex model, which allows to retrieve the vortex characteristics, including its radius, vorticity, and position of the center. At all Reynolds numbers, the near-wall region is found to be the most densely populated region, predominantly with streamwise vortices that are on average smaller and more intense than spanwise vortices. In contrast, the logarithmic region is equally constituted of streamwise and spanwise vortices having equivalent characteristics. Two different scalings were employed to analyze the vortex radius and vorticity: the wall unit scaling and the Kolmogorov scaling. In wall unit scaling, a good universality in Reynolds numbers of the vortices radius and vorticity is observed in the near-wall and logarithmic regions: the vorticity is found to be maximum at the wall, decreasing first rapidly and then increasing slowly with wall-normal distance; the radius is increasing slowly with wall-normal distance in both the regions, except for the streamwise vortices, for which a sharp increase in radius is observed in the near-wall region. However, wall units scaling is found to be deficient in the outer region, where Reynolds number effects are observed. The Kolmogorov scaling appears to be universal both in Reynolds number and wall-normal distance across the investigated three regions, with a mean radius of the order of 8η and a mean vorticity of the order of 1.5τ⁻¹, but for the SPIV data only. In the DNS dataset, the radius in the Kolmogorov scaling slowly decreases with wall-normal distance. This difference between the SPIV and DNS datasets may be linked to a difference between the boundary layer flow and the channel flow, rather than to the techniques themselves. Finally, the distribution of the vorticity of the detected vortices seems to follow faithfully a log-normal distribution, in good agreement with Kolmogorov’s theory (A refinement of previous hypothesis concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number, J. Fluid Mech. 13 (1962), pp. 82–85).

Keywords:

• coherent structures
• near-wall turbulence
• vortical structures
• particle image velocimetry
• direct numerical simulation

Acknowledgements

Financial support from CNRS, ‘Region Nord pas de Calais’, the Australian Research Council, as well as ‘Ecole Centrale de Lille’, and the French embassy in Australia is also gratefully acknowledged.