Journal of Fluid Mechanics

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Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

G. E. ELSINGAa1 c1, R. J. ADRIANa2, B. W. VAN OUDHEUSDENa1 and F. SCARANOa1

a1 Department of Aerospace Engineering, Delft University of Technology, 2629HS Delft, The Netherlands

a2 Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ85287, USA

Abstract

Tomographic particle image velocimetry was used to quantitatively visualize the three-dimensional coherent structures in a supersonic (Mach 2) turbulent boundary layer in the region between y/δ = 0.15 and 0.89. The Reynolds number based on momentum thickness Reθ = 34000. The instantaneous velocity fields give evidence of hairpin vortices aligned in the streamwise direction forming very long zones of low-speed fluid, consistent with Tomkins & Adrian (J. Fluid Mech., vol. 490, 2003, p. 37). The observed hairpin structure is also a statistically relevant structure as is shown by the conditional average flow field associated to spanwise swirling motion. Spatial low-pass filtering of the velocity field reveals streamwise vortices and signatures of large-scale hairpins (height > 0.5δ), which are weaker than the smaller scale hairpins in the unfiltered velocity field. The large-scale hairpin structures in the instantaneous velocity fields are observed to be aligned in the streamwise direction and spanwise organized along diagonal lines. Additionally the autocorrelation function of the wall-normal swirling motion representing the large-scale hairpin structure returns positive correlation peaks in the streamwise direction (at 1.5δ distance from the DC peak) and along the 45° diagonals, which also suggest a periodic arrangement in those directions. This is evidence for the existence of a spanwise–streamwise organization of the coherent structures in a fully turbulent boundary layer.

(Received November 05 2008)

(Revised September 08 2009)

(Accepted September 08 2009)

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