Statistical analysis of low- and high-speed large-scale structures in the outer region of an adverse pressure gradient turbulent boundary layer

Abstract

Two-point correlations and quadrant two-point correlations (termed and introduced by authors) have been employed in order to study low- and high-speed large-scale structures in the outer region of a turbulent boundary layer subjected to a strong adverse pressure gradient. They are computed with particle image velocimetry (PIV) data comprising of large sets of streamwise-spanwise instantaneous velocity fields at three wall-normal positions (0.2δ, 0.5δ, 0.8δ; δ is the boundary layer thickness) at three different streamwise locations in the adverse-pressure-gradient zone, from downstream of the strong suction peak up to detachment. Two-point correlations of the streamwise velocity fluctuation confirm the existence of alternating zones of high- and low-speed fluid in the middle (0.5δ) and lower (0.2δ) parts of the outer region similar to those observed in the log and wake regions of zero-pressure-gradient turbulent boundary layers. However, the negative-positive-negative pattern of these two-point correlations disappears in the lower part (0.2δ) of the large-velocity-defect zone, i.e. near detachment. In the latter region, the results support the existence of large-scale u-structures, many of which are streamwise elongated, that meander more or are less streamwise aligned than the u-structures elsewhere. The ratio of streamwise to spanwise length scales associated with the two-point correlations reveals that u-structures in the zero-pressure-gradient cases are more elongated in the streamwise direction than those in the adverse-pressure-gradient cases, especially in the lower part of the boundary layer. The quadrant two-point analysis allows us to discriminate events with respect to the sign of the streamwise velocity fluctuation at the reference and second points in the two-point correlation function. By using this technique, it is found that in the lower part of the outer region, i.e. 0.2δ (in the upper part of boundary layer, i.e. 0.8δ), large-scale high-speed events (low-speed events) are more intense than low-speed (high-speed) ones and also contribute more to the two-point correlations. In the middle of the boundary layer where the maximum turbulence activity occurs, large-scale low- and high-speed motions have comparable intensities and frequencies of occurrence. However, the low-speed events are slightly more intense and seem to be spatially more coherent.

Keywords:

• turbulent boundary layer
• adverse pressure gradient
• large-scale structures
• two-point correlations
• particle image velocimetry

Acknowledgements

Financial support from NSERC and CFI of Canada is gratefully acknowledged by the authors. They also wish to thank C.D. Tomkins and R.J. Adrian for sharing their data, as well as G. Routhier, M.H. Shafiei Mayam and C. Chabot for their help with the measurements and data processing.