Published online by Cambridge University Press: 13 April 2018
The mechanism underlying the coherent hairpin process in wall-bounded shear flows is studied. An algorithm for the identification and analysis of flow structures based on morphological operations is presented. The method distils the topology of the flow field into a discrete data set and enables the time-resolved sampling of coherent flow processes across multiple scales. Application to direct simulation data of transitional and turbulent boundary layers at moderate Reynolds number sheds light on the flow physics of the hairpin process. The analysis links the hairpin to an exponential instability which is amplified in the flow distorted by a negative perturbation in the streamwise velocity component. Linear analyses substantiate the connection to an inviscid instability mechanism of varicose type. The formation of packets of hairpins is related to a self-similar process which originates from a single patch of low-speed fluid and describes a recurrence of the dynamics that leads to the formation of an individual hairpin. Analysis of the evolution of several thousand turbulent hairpins provides a statistical characterization of the principal dynamics and yields a time-resolved average of the hairpin process. Comparisons with the transitional hairpin show qualitatively consistent trends and thus support earlier hypotheses of their equivalence. In terms of the causality of events, the results suggest that the hairpin is a manifestation of the varicose instability and as such is a consequence rather than a cause of the primary perturbations of the flow.
Animation of hairpin formation during the late stage of K-type transition. Isosurfaces of $Q=5$ (red), $u'=0.20$ (white) and $u'=-0.20$ (black).
Animation of hairpin formation during the late stage of K-type transition. Isosurfaces of $Q=5$ (red),
Animation of the dynamically averaged turbulent hairpin process. Isosurfaces of $Q$ criterion (red) and positive (white) and negative (black) streamwise velocity fluctuations $u'$.