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Physics of Fluids / Volume 19 / Issue 4 / AWARD AND INVITED PAPERS
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Phys. Fluids 19, 041301 (2007); http://dx.doi.org/10.1063/1.2717527 (16 pages)

Hairpin vortex organization in wall turbulence a

a This paper is based on the Otto Laporte Award Lecture, presented by the author at the 58th Annual American Physical Society Division of Fluid Dynamics Meeting, which was held 20–22 November 2005 in Chicago, IL.
Ronald J. Adrian

Laboratory for Energetic Flow and Turbulence, Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, Arizona 85287

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(Received 31 October 2006; accepted 13 February 2007; published online 18 April 2007)

Coherent structures in wall turbulence transport momentum and provide a means of producing turbulent kinetic energy. Above the viscous wall layer, the hairpin vortex paradigm of Theodorsen coupled with the quasistreamwise vortex paradigm have gained considerable support from multidimensional visualization using particle image velocimetry and direct numerical simulation experiments. Hairpins can autogenerate to form packets that populate a significant fraction of the boundary layer, even at very high Reynolds numbers. The dynamics of packet formation and the ramifications of organization of coherent structures (hairpins or packets) into larger-scale structures are discussed. Evidence for a large-scale mechanism in the outer layer suggests that further organization of packets may occur on scales equal to and larger than the boundary layer thickness.

© 2007 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. NEAR-WALL HAIRPIN EDDY PARADIGM
  3. HAIRPIN VORTEX PACKETS
  4. STATISTICAL EVIDENCE FOR PACKETS
  5. LARGE SCALES OF MOTION
  6. SUMMARY

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KEYWORDS and PACS

Keywords

vortices, boundary layer turbulence, flow visualisation, flow simulation

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.2717527

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (click on thumbnails to view enlargements)

FIG.1
Profiles of shear stresses and net force due to Reynolds shear stress math in fully developed pipe and channel flow. The profiles are qualitatively similar for the boundary layer. The contributions to −math arise from the probability density function’s bias toward events in the second and fourth quadrant of the u-v plane.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
(a) Smoke visualization of the streamwise-wall-normal plane in a turbulent boundary layer showing various eddy structures (from Ref. 5); (b) H2 bubble visualization of low-speed streaks in a streamwise-spanwise plane (from Ref. 11).

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
(Color) (a) Theodorsen’s (1952) depiction of a horseshoe vortex (from Ref. 9); (b) sketch of “The Horseshoe” attributed to Weske (courtesy of J. Wallace, University of Maryland); (c) Robinson’s summary of structures found in direct numerical simulation of wall turbulence (from Ref. 12).

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FIG.4
(Color) Conditional average of the flow around a Q2 event velocity vector (u,v,0) located at y+ = 49 in a direct numerical simulation of channel flow at Reτ = 300. The surface is an iso-contour of the turbulent swirling strength,λci, and the vectors denote fluctuations. (a) top view; (b) oblique view (from Ref. 31).

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.5
(a) Schematic of a hairpin eddy attached to the wall; (b) signature of the hairpin eddy in the streamwise-wall-normal plane (from Ref. 33).

FIG.5 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.6
Hairpin vortex signatures in a PIV measurement of flow in the streamwise-wall-normal plane of a turbulent boundary layer, Reθ = 930. The heads of the hairpins are labeled A, B, C, and D. Note the correspondence between the flow patterns below and behind each head with the hairpin signature sketched in Fig. 5b. Zones of uniform momentum are labeled I, II, and III. The reference frame for the vectors is translating at 80% of the free-stream velocity (from Ref. 33).

FIG.6 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.7
(Color online) (a) Packet of hairpins that evolves from a conditional Q2 event (w = 0) similar to that shown in Fig. 4. The shaded surfaces are isosurfaces of the swirling strength. The time is 297 viscous time scales after the initial condition, and the channel flow Reynolds number is Reτ = 180 (from Ref. 37). (b) Last frame of the digital movie. Evolution of a packet of hairpins from a conditional Q2 event similar to that shown in Fig. 4. Surface is an isosurface of the swirling strength. The Reynolds number is Reτ = 395 (courtesy of K. Kim) (enhanced online).

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FIG.8
(Color) Chaotic packet of hairpins that evolves from an initial conditional Q2 event (w = 0) similar to that shown in Fig. 4 with 5% noise added to simulate growth in a slightly turbulent environment. The time is 355 viscous time scales after the initial condition and the channel flow Reynolds number is Reτ = 395 (courtesy of K. Kim) (enhanced online).

FIG.8 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.9
Hairpin packets can be observed in DNS of fully turbulent channel flows. Reτ = 300. The heads of hairpins that appear to be members of one or perhaps two packets are indicated in white. Note the large amount of disorganized small-scale clutter (from Ref. 31).

FIG.9 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.10
(Color) Hairpin packets are observed very commonly in high Reynolds number laboratory flows. The PIV data in this figure show that long packets occur inside even larger packets. The color contours are swirling strength in the lower plot and spanwise vorticity in the upper, expanded plot. The vectors are total velocity minus 76% of the free stream velocity (lower plot) and 79% of the free-stream velocity (upper plot) (from Ref. 33).

FIG.10 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.11
(Color) (a) Ramp-shaped patterns consistent with hairpin packets such as those in Fig. 10 can also be found in the atmospheric boundary layer. Smoke emitted from the floor of Utah’s Great Salt Lake desert is illuminated in the streamwise-wall-normal plane by a Nd: YAG laser light sheet. The scale is 2 m from the floor to the top of the figure. The PIV visualization of the laboratory boundary layer from Fig. 10 is shown for comparison (from Ref. 45). (b) Video sequence of the ramps observed in the atmospheric boundary layer described in (a) (enhanced online).

FIG.11 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.12
(Color) Conceptual scenario of hairpins attached to the wall and growing in an environment of overlying larger hairpin packets (from Ref. 33).

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FIG.13
(Color) Long streaks of low-momentum fluid in streamwise-spanwise planes of boundary layer flow at y/δ = 0.2 and Reθ = 2216. The red (blue) contours represent regions of swirling strength with counterclockwise (clockwise) rotation that tend to occur to the right (left) of the low-speed streaks (from Ref. 56).

FIG.13 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.14
Spanwise merger of hairpins by vortex reconnection of legs (from Ref. 63).

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FIG.15
(Color) (a) Visualization of multiscale motion in pipe flow using smoke injected at y/R = 0.05; (bottom) large-scale low-speed steak in the streamwise-spanwise plane; (top) view of the streamwise-wall-normal plane; (inset) expanded view of hairpins in the low-speed streak (from Ref. 62). (b) Sketch of small scales clustered between spanwise wall flows from larger-scale eddies.

FIG.15 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.16
Summary sketch of the organization of hairpins and packets in a boundary layer. Hairpin packets are most common in the lower half of the boundary layer, especially the logarithmic layer, creating uniform momentum zones in layers. They sometimes extend to the edge of the boundary layer and the largest ones may be the source of turbulent bulges. Detached, smaller-scale hairpin vortices can be created by shear at the turbulent-nonturbulent interface and possibly within the bulk of the layer.

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