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

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 Re θ = 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.