Spanwise growth of vortex structure in wall turbulence

Recent studies of the structure of wall turbulence have lead to the development of a conceptual model that validates and integrates many elements of previous models into a relatively simple picture based on self-assembling packets of hairpin vortex eddies. By continually spawning new hairpins the packets grow longer in the streamwise direction, and by mutual induction between adjacent hairpins the hairpins are strained so that they grow taller and wider as they age. The result is a characteristic growth angle in the streamwise-wall normal plane. The spanwise growth of individual packets implies that packets must either merge or pass through each other when they come into contact. Direct numerical simulations of the growth and interaction of spanwise adjacent hairpins shows that they merge by the vortex connection mechanism originally proposed by Wark and Nagib (1990). In this mechanism the quasi-streamwise legs of two hairpins annihilate each other, by virtue of having opposite vorticity, leaving a new hairpin of approximately double the width of the individuals. PIV measurements in planes parallel to the wall support this picture. DNS of multiple hairpins shows how the spanwise scale doubles when the hairpins form an array.