Abstract
Laboratory experiments were performed to characterize the distinct features of hairpin-like vortical structures induced via pulsed, wall-normal jets in laminar (LBL), and turbulent boundary layers (TBLs). Hotwire anemometry was used to characterize the disturbed flow at multiple streamwise, transverse, and vertical locations. The dominant spatiotemporal structure of the induced motions was reconstructed using Taylor’s hypothesis and time-averaged, phase-locked data. Results support the concept that the meandering of very-long, low-momentum streaks observed in the logarithmic layer and lower part of wake regions of TBLs results from the upwash of hairpin vortices or packets. Comparing the induced hairpin-like vortices in the LBL and TBL reveals the modulation of the mean shear; using the second-order derivative of the mean streamwise velocity, we show a linkage between the mean shear gradient and appearance of low- and high-momentum streaks in the logarithmic layer. Streamwise velocity profiles with a pitot tube by Smith (Effect of Reynolds number on the structure of turbulent boundary layers, 1994) at ten Reynolds numbers from Reθ = 4601 to 13,189 are also inspected to evaluate such linkage in a broader range of Re. As Reynolds number increased, the vertical regions of the negative second derivative of mean streamwise velocity increased. The minimum value of mean shear gradient decreased, indicating that the mean shear stress gradient increased to form more noticeable low- and high-momentum streaks in the logarithmic layer. Besides, the Reynolds tensor’s principal stresses and principal axes angles associated with the hairpin vortex legs stretching are demonstrated by DNS data (Spalart, P. R. 1988) as Reynolds number increased.
Graphic abstract
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Acarlar MS, Smith CR (1987a) A study of hairpin vortices in a laminar boundary layer. I-hairpin vortices generated by a Hemisphere protuberance. J Fluid Mech 175:1–41. https://doi.org/10.1017/s0022112087000272
Acarlar MS, Smith CR (1987b) A study of hairpin vortices in a laminar boundary layer. II-hairpin vortices generated by fluid injection. J Fluid Mech 175:43–83. https://doi.org/10.1017/s0022112087000284
Adrian RJ (2007) Hairpin vortex organization in wall turbulence. Phys Fluids 19:041301. https://doi.org/10.1063/1.2717527
Adrian RJ, Meinhart CD, Tomkins CD (2000) Vortex organization in the outer region of the turbulent boundary layer. J Fluid Mech 422:1–54. https://doi.org/10.1017/s0022112000001580
Chang YK, Vakilia AD (1995) Dynamics of vortex rings in crossflow. Phys Fluids 7(7):1583–1597. https://doi.org/10.1063/1.868545
Christensen KT, Adrian RJ (2001) Statistical evidence of hairpin vortex packets in wall turbulence. J Fluid Mech 431:433–443. https://doi.org/10.1017/s0022112001003512
Del Alamo JC, Jiménez J, Zandonade P, Moser RD (2004) Scaling of the energy spectra of turbulent channels. J Fluid Mech 500:135–144. https://doi.org/10.1017/s002211200300733x
Eitel-Amor G, Örlü R, Schlatter P, Flores O (2015) Hairpin vortices in turbulent boundary layers. Phys Fluids 27:025108. https://doi.org/10.1063/1.4907783
Elsinga GE, Adrian RJ, van Oudheusden B.W, Scarano F (2007) Tomographic-PIV investigation of a high Reynolds number turbulent boundary layer. In: 7th international symposium on particle image velocimetry, Rome, Italy, 11–14 September 2007
Ganapathisubramani B, Longmire EK, Marusic I (2003) Characteristics of vortex packets in turbulent boundary layers. J Fluid Mech 478:35–46. https://doi.org/10.1017/s0022112002003270
Giovanetti M, Sung HJ, Hwang Y (2017) Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions. J Fluid Mech 832:483–513. https://doi.org/10.1017/jfm.2017.697
Guala M, Metzger M, McKeon BJ (2011) Interactions within the turbulent boundary layer at high Reynolds number. J Fluid Mech 666:573–604. https://doi.org/10.1017/s0022112010004544
Hamilton JM, Kim J, Waleffe F (1995) Regeneration mechanisms of near-wall turbulence structures. J Fluid Mech 287:317–348. https://doi.org/10.1017/s0022112095000978
Hutchins N, Choi K-S (2002) Accurate measurements of local skin friction coefficient using hotwire anemometry. Prog Aerosp Sci 38:421–446. https://doi.org/10.1016/S0376-0421(02)00027-1
Hutchins N, Marusic I (2007) Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J Fluid Mech 579:1–28. https://doi.org/10.1017/s0022112006003946
Hutchins N, Monty JP, Ganapathisubramani B, Ng HCH, Marusic I (2011) Three dimensional conditional structure of a high Reynolds number turbulent boundary layer. J Fluid Mech 673:255–285. https://doi.org/10.1017/s0022112010006245
Hwang Y, Bengana Y (2016) Self-sustaining process of minimal attached eddies in turbulent channel flow. J Fluid Mech 795:708–738. https://doi.org/10.1017/jfm.2016.226
Jiménez J (2013) Near wall turbulence. Phys Fluids 25:101302. https://doi.org/10.1063/1.4824988
Jiménez J (2015) Direct detection id linearized bursts in turbulence. Phys Fluids 27:065102. https://doi.org/10.1063/1.4921748
Kim K, Sung HJ, Adrian RJ (2008) Effects of background noise on generating coherent packets of hairpin vortices. Phys Fluids 20:105107. https://doi.org/10.1063/1.3001797
Krueger PS, Ghari M (2003) The significance of vortex ring formation to the impulse and thrust of a starting jet. Phys Fluids 15(5):1271–1281. https://doi.org/10.1063/1.1564600
Marusic I, Hutchins N (2008) Study of the log-layer structure in wall turbulence over a very large range of reynolds number. Flow Turbul Combust 81:115–130. https://doi.org/10.1007/s10494-007-9116-0
Mathis R, Hutchins N, Marusic I (2009) Large scale amplitude modulation of the small scale structures in turbulent boundary layers. J Fluid Mech 628:311–337. https://doi.org/10.1017/s0022112009006946
Monty JP, Stewart JA, Willams RC, Chong MS (2007) Large-scale features in turbulent pipe and channel flows. J Fluid Mech 589:147–156. https://doi.org/10.1017/s002211200700777x
Natrajan VK, Christensen KT (2006) The role of coherent structures in subgrid-scale energy transfer within the log layer of wall turbulence. Phys Fluids 18:065104. https://doi.org/10.1063/1.2206811
Robinson SK (1991) Coherent motions in the turbulent boundary layer. Annu Rev Fluid Mech 23:601–639. https://doi.org/10.1146/annurev.fl.23.010191.003125
Sabatino DR, Maharjan R (2015a) Characterizing the formation and regeneration of hairpin vortices in a laminar boundary layer. Phys Fluids 27:124104. https://doi.org/10.1063/1.4936138
Sabatino DR, Maharjan R (2015b) Characterizing the formation and regeneration of hairpin vortices in a laminar boundary layer. Phys Fluids 27:124104. https://doi.org/10.1063/1.4936138
Samie M, Marusic I, Hutchins N, Fu MK, Fan Y, Harltmark M, Smits AJ (2018) Fully resolved measurements of turbulent boundary layer flows up tp Reτ = 20000. J Fluid Mech 851:391–415. https://doi.org/10.1017/jfm.2018.508
Sanmiguel Vila C, Vinuesa R, Discetti S, Ianiro A, Schlatter P, Örlü R (2017) On the identification of well-behaved turbulent boundary layers. J Fluid Mech 822:109–138. https://doi.org/10.1017/jfm.2017.258
Sau R, Mahesh K (2008) Dynamics and mixing of vortex rings in crossflow. J Fluid Mech 604:389–409. https://doi.org/10.1017/s0022112008001328
Schlatter P, Örlü R (2012) Turbulent boundary layers at moderate Reynolds numbers: inflow length and tripping effects. J Fluid Mech 710:5–34. https://doi.org/10.1017/jfm.2012.324
Schlichting H (1968) Boundary layer theory. McGraw-Hill, New York
Schoppa W, Hussain F (2002) Coherent structure generation in near-wall turbulence. J Fluid Mech 453:57–108. https://doi.org/10.1017/s002211200100667x
Schwarz AC, Plesniak MW, Murthy SNB (2002) Response of turbulent boundary layers to multiple strain rate. J Fluid Mech 458:333–377. https://doi.org/10.1017/s0022112002007863
Shekar A, Graham MD (2018) Exact coherent states with hairpin-like vortex structure in channel flow. J Fluid Mech 849:76–89. https://doi.org/10.1017/jfm.2018.409
Shur ML, Strelets MK, Travin AK, Spalart PR (2000) Turbulence modeling in rotating and curved channels: assessing the Spalart-Shur correction. AIAA 38:784–792. https://doi.org/10.2514/2.1058
Silva CM, Krug D, Lohse D, Marusic I (2017) Universality of the energy-containing structures in wall-bounded turbulence. J Fluid Mech 823:498–510. https://doi.org/10.1017/jfm.2017.315
Smith RW (1994) Effect of Reynolds number on the structure of turbulent boundary layers. Ph.D. thesis, Department of Mechanical and Aerospace Engineering, Princeton University
Spalart PR (1988) Direct simulation of a turbulent boundary layer up to Rθ=1410. J Fluid Mech 187:61–98. https://doi.org/10.1017/s0022112088000345
Spalart PR, Shur M (1997) On the sensitization of turbulence models to rotation and curvature. Aerosp Sci Technol 1(5):297–302. https://doi.org/10.1016/S1270-9638(97)90051-1
Suponitsky V, Cohen J, Bar-Yoseph PZ (2005) The generation of streaks and hairpin vortices from a localized vortex disturbance embedded in unbounded uniform shear flow. J Fluid Mech 535:65–100. https://doi.org/10.1017/s0022112005004453
Tomkins CD, Adrian RJ (2003) Spanwise structure and scale growth in turbulent boundary layers. J Fluid Mech 490:37–74. https://doi.org/10.1017/s0022112003005251
Zhou J, Adrian RJ, Balachandar S (1996) Autogeneration of near-wall vortical structures in channel flow. Phys Fluids 8(1):288–290. https://doi.org/10.1063/1.868838
Zhou J, Adrian RJ, Balachandar S, Kendall TM (1999) Mechanisms for generating coherent packets of hairpin vortices in channel flow. J Fluid Mech 387:353–396. https://doi.org/10.1017/S002211209900467X
Acknowledgements
The first author would like to acknowledge the financial support from the National Natural Science Foundation of China (Grant Nos. 91952301 and 91852101).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Liu, JH., Jiang, N. & Chamorro, L.P. On the large-scale streaks in the logarithmic layer of wall-bounded flows. J Vis 25, 511–520 (2022). https://doi.org/10.1007/s12650-021-00810-x
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12650-021-00810-x