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Statistical and structural similarities between micro- and macro-scale wall turbulence

Department of Theoretical and Applied Mechanics (UIUC)
Publication Date
  • Wall Turbulence
  • Mathematics


Microscopic particle-image velocimetry (micro-PIV) measurements are made in the streamwise–wall-normal plane of a 536-micron capillary at Re = 4500 to study the statistical and structural features of wall turbulence at the microscale. Single-point velocity statistics, including the mean velocity profile, the root-mean-square streamwise and wall-normal velocities, and the Reynolds shear stress profile, agree well with established direct numerical simulations of turbulence in the same geometry at Re = 5300. This consistency validates the efficacy of micro-PIV as an experimental tool for studying instantaneous, and even turbulent, flow behavior at the microscale. The instantaneous micro-PIV velocity fields reveal spanwise vortices that streamwise-align to form larger-scale interfaces that are inclined slightly away from the wall. These observations are entirely consistent with the signatures of hairpin vortices and hairpin vortex packets that are often noted in instantaneous PIV realizations of macroscale wall turbulence. Further, two-point velocity correlations and estimates of the conditionally-averaged velocity field given the presence of a spanwise vortex indicate that hairpin structures and their organization into larger-scale vortex packets are statistically-significant features of wall turbulence at the microscale.

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