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Wall-attached structures of velocity fluctuations in a turbulent boundary layer

Published online by Cambridge University Press:  12 October 2018

Jinyul Hwang  and
Hyung Jin Sung Open the ORCID record for Hyung Jin Sung [Opens in a new window]
Jinyul Hwang
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
Hyung Jin Sung*
Affiliation:
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea
*
†Email address for correspondence: [email protected]
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Abstract

Wall turbulence is a ubiquitous phenomenon in nature and engineering applications, yet predicting such turbulence is difficult due to its complexity. High-Reynolds-number turbulence arises in most practical flows, and is particularly complicated because of its wide range of scales. Although the attached-eddy hypothesis postulated by Townsend can be used to predict turbulence intensities and serves as a unified theory for the asymptotic behaviours of turbulence, the presence of coherent structures that contribute to the logarithmic behaviours has not been observed in instantaneous flow fields. Here, we demonstrate the logarithmic region of the turbulence intensity by identifying wall-attached structures of the velocity fluctuations ($u_{i}$) through the direct numerical simulation of a moderate-Reynolds-number boundary layer ($Re_{\unicode[STIX]{x1D70F}}\approx 1000$). The wall-attached structures are self-similar with respect to their heights ($l_{y}$), and in particular the population density of the streamwise component ($u$) scales inversely with $l_{y}$, reminiscent of the hierarchy of attached eddies. The turbulence intensities contained within the wall-parallel components ($u$ and $w$) exhibit the logarithmic behaviour. The tall attached structures ($l_{y}^{+}>100$) of $u$ are composed of multiple uniform momentum zones (UMZs) with long streamwise extents, whereas those of the cross-stream components ($v$ and $w$) are relatively short with a comparable width, suggesting the presence of tall vortical structures associated with multiple UMZs. The magnitude of the near-wall peak observed in the streamwise turbulent intensity increases with increasing $l_{y}$, reflecting the nested hierarchies of the attached $u$ structures. These findings suggest that the identified structures are prime candidates for Townsend’s attached-eddy hypothesis and that they can serve as cornerstones for understanding the multiscale phenomena of high-Reynolds-number boundary layers.

JFM classification

Turbulent Flows: Turbulent boundary layers Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 856 , 10 December 2018 , pp. 958 - 983
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Copyright
© 2018 Cambridge University Press 

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References

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.Google Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.Google Scholar
Ahn, J., Lee, J. H., Lee, J., Kang, J.-H. & Sung, H. J. 2015 Direct numerical simulation of a 30R long turbulent pipe flow at Re 𝜏 = 3008. Phys. Fluids 27 (6), 065110.Google Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329–358.Google Scholar
Avila, K., Moxey, D., de Lozar, A., Avila, M., Barkley, D. & Hof, B. 2011 The onset of turbulence in pipe flow. Science 333 (6039), 192–196.Google Scholar
Baars, W. J., Hutchins, N. & Marusic, I. 2017 Self-similarity of wall-attached turbulence in boundary layers. J. Fluid Mech. 823, R2.Google Scholar
Baltzer, J. R., Adrian, R. J. & Wu, X. 2013 Structural organization of large and very large scales in turbulent pipe flow simulation. J. Fluid Mech. 720, 329–358.Google Scholar
Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M. & Hof, B. 2015 The rise of fully turbulent flow. Nature 526 (7574), 550–553.Google Scholar
Chandra, D., Baidya, R., Monty, J. P. & Marusic, I. 2017 Two-dimensional energy spectra in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 826, R1.Google Scholar
Chauhan, K., Philip, J., de Silva, C. M., Hutchins, N. & Marusic, I. 2014 The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119–151.Google Scholar
DeGraaff, D. B. & Eaton, J. K. 2000 Reynolds number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319–346.Google Scholar
Ganapathisubramani, B., Hutchins, N., Monty, J. P., Chung, D. & Marusic, I. 2012 Amplitude and frequency modulation in wall turbulence. J. Fluid Mech. 712, 61–91.Google Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layer. J. Fluid Mech. 478, 35–46.Google Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20, 124–132.Google Scholar
Fiscaletti, D., de Kat, R. & Ganapathisubramani, B. 2018 Spatial–spectral characteristics of momentum transport in a turbulent boundary layer. J. Fluid Mech. 836, 599–634.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanism of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.Google Scholar
Hellström, L. H. O., Marusic, I. & Smits, A. J. 2016 Self-similarity of the large-scale motions in turbulent pipe flow. J. Fluid Mech. 792, R1.Google Scholar
Hof, B., van Doorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F. 2004 Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305 (5690), 1594–1598.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Hultmark, M., Vallikivi, M., Bailey, S. C. C. & Smits, A. J. 2012 Turbulent pipe flow at extreme Reynolds numbers. Phys. Rev. Lett. 108 (9), 094501.Google Scholar
Hutchins, N., Hambleton, W. T. & Marusic, I. 2005 Inclined cross-stream stereo particle image velocimetry measurements in turbulent boundary layers. J. Fluid Mech. 541, 21–54.Google Scholar
Hutchins, N. & Marusic, I. 2007a Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.Google Scholar
Hutchins, N. & Marusic, I. 2007b Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 647–664.Google Scholar
Hwang, J., Lee, J. & Sung, H. J. 2016a Influence of large-scale accelerating motions on turbulent pipe and channel flows. J. Fluid Mech. 804, 420–441.Google Scholar
Hwang, J., Lee, J., Sung, H. J. & Zaki, T. A. 2016b Inner–outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128–157.Google Scholar
Hwang, J. & Sung, H. J. 2017a Influence of large-scale motions on the frictional drag in a turbulent boundary layer. J. Fluid Mech. 829, 751–779.Google Scholar
Hwang, J. & Sung, H. J. 2017b Wall-attached structures of streamwise velocity fluctuations in turbulent boundary layer. Bull. Am. Phys. Soc. 62.Google Scholar
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254–289.Google Scholar
Hwang, Y. 2016 Mesolayer of attached eddies in turbulent channel flow. Phys. Rev. Fluids 1, 064401.Google Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44, 27–45.Google Scholar
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 101302.Google Scholar
Jiménez, J., del Álamo, J. C. & Flores, O. 2004 The large-scale dynamics of near-wall turbulence. J. Fluid Mech. 505, 179–199.Google Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.Google Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds number. J. Fluid Mech. 657, 335–360.Google Scholar
Kawahara, G., Uhlmann, M. & Van Veen, L. 2012 The significance of simple invaraiant solutions in turbulent flows. Annu. Rev. Fluid Mech. 44, 203–225.Google Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417–422.Google Scholar
Kim, K., Baek, S. J. & Sung, H. J. 2002 An implicit velocity decoupling procedure for the incompressible Navier–Stokes equations. Intl J. Numer. Meth. Fluids 38 (2), 125–138.Google Scholar
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Runstadler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30 (4), 741–773.Google Scholar
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283–325.Google Scholar
Krug, D., Yang, X. I. A., de Silva, C. M., Ostilla-Mónico, R., Verzicco, R., Marusic, I. & Lohse, D. 2017 Statistics of turbulence in the energy-containing range of Taylor–Couette compared to canonical wall-bounded flows. J. Fluid Mech. 830, 797–819.Google Scholar
Kwon, Y. S., Hutchins, N. & Monty, J. P. 2016 On the use of the Reynolds decomposition in the intermittent region of turbulent boundary layers. J. Fluid Mech. 794, 5–16.Google Scholar
Kwon, Y. S., Philip, J., de Silva, C. M., Hutchins, N. & Monty, J. P. 2014 The quiescent core of turbulent channel flow. J. Fluid Mech. 751, 228–254.Google Scholar
Laskari, A., de Kat, R., Hearst, R. J. & Ganapathisubramani, B. 2018 Time evolution of uniform momentum zones in a turbulent boundary layer. J. Fluid Mech. 842, 554–590.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395–415.Google Scholar
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100–130.Google Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13 (3), 735–743.Google Scholar
Marusic, I., Baars, W. J. & Hutchins, N. 2017 Scaling of the streamwise turbulence intensity in the context of inner–outer interactions in wall turbulence. Phys. Rev. Fluids 2 (10), 100502.Google Scholar
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15 (8), 2461–2464.Google Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329 (5988), 193–196.Google Scholar
Marusic, I. & Monty, J. P. 2018 Attached eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 49–74.Google Scholar
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.Google Scholar
Meinhart, C. D. & Adrian, R. J. 1995 On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7 (4), 694–696.Google Scholar
Millikan, C. B. 1938 A critical discussion of turbulent flow in channels and circular tubes. In Proceedings of 5th International Congress on Applied Mechanics (Cambridge, MA, 1938), pp. 386–392. Wiley.Google Scholar
Moisy, F. & Jiménez, J. 2004 Geometry and clustering of intense structures in isotropic turbulence. J. Fluid Mech. 513, 111–133.Google Scholar
Morrill-Winter, C., Philip, J. & Klewicki, J. 2017 Statistical evidence of anasymptotic geometric structure to the momentum transporting motions in turbulent boundary layers. Phil. Trans. R. Soc. Lond. A 375 (2089), 20160084.Google Scholar
Nickels, T. B. & Marusic, I. 2001 On the different contributions of coherent structures to the spectra of a turbulent round jet and a turbulent boundary layer. J. Fluid Mech. 448, 367–385.Google Scholar
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the k 1 -1 law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95 (7), 074501.Google Scholar
Örlü, R., Fiorini, T., Segalini, A., Bellani, G., Talamelli, A. & Alfredsson, P. H. 2017 Reynolds stress scaling in pipe flow turbulence: first results from CICLoPE. Phil. Trans. R. Soc. A 375 (2089), 20160187.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173–217.Google Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Perry, A. E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298, 361–388.Google Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.Google Scholar
Sillero, J. A., Jiménez, J. & Moser, R. D. 2013 One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ ≈ 2000. Phys. Fluids 25 (10), 105102.Google Scholar
de Silva, C. M., Hutchins, N. & Marusic, I. 2016 Uniform momentum zones in turbulent boundary layers. J. Fluid Mech. 786, 309–331.Google Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Vallikivi, M., Ganapathisubramani, B. & Smits, A. J. 2015 Spectral scaling in boundary layers and pipes at very high Reynolds numbers. J. Fluid Mech. 771, 303–326.Google Scholar
Yoon, M., Hwang, J. & Sung, H. J. 2018 Contribution of large-scale motions to the skin friction in a moderate adverse pressure gradient turbulent boundary layer. J. Fluid Mech. 848, 288–311.Google Scholar