Hostname: page-component-5d59c44645-mrcq8 Total loading time: 0 Render date: 2024-02-27T11:58:27.128Z Has data issue: false hasContentIssue false

Very-large-scale motions in a turbulent boundary layer

Published online by Cambridge University Press:  17 February 2011

Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-Gu, Daejeon 305-701, Republic of Korea
Department of Mechanical Engineering, KAIST, 291 Daehak-ro, Yuseong-Gu, Daejeon 305-701, Republic of Korea
Email address for correspondence:


Direct numerical simulation of a turbulent boundary layer was performed to investigate the spatially coherent structures associated with very-large-scale motions (VLSMs). The Reynolds number was varied in the range Reθ = 570–2560. The main simulation was conducted by using a computational box greater than 50δo in the streamwise domain, where δo is the boundary layer thickness at the inlet, and inflow data was obtained from a separate inflow simulation based on Lund's method. Inspection of the three-dimensional instantaneous fields showed that groups of hairpin vortices are coherently arranged in the streamwise direction and that these groups create significantly elongated low- and high-momentum regions with large amounts of Reynolds shear stress. Adjacent packet-type structures combine to form the VLSMs; this formation process is attributed to continuous stretching of the hairpins coupled with lifting-up and backward curling of the vortices. The growth of the spanwise scale of the hairpin packets occurs continuously, so it increases rapidly to double that of the original width of the packets. We employed the modified feature extraction algorithm developed by Ganapathisubramani, Longmire & Marusic (J. Fluid Mech., vol. 478, 2003, p. 35) to identify the properties of the VLSMs of hairpin vortices. In the log layer, patches with the length greater than 3δ–4δ account for more than 40% of all the patches and these VLSMs contribute approximately 45% of the total Reynolds shear stress included in all the patches. The VLSMs have a statistical streamwise coherence of the order of ~6δ; the spatial organization and coherence decrease away from the wall, but the spanwise width increases monotonically with the wall-normal distance. Finally, the application of linear stochastic estimation demonstrated the presence of packet organization in the form of a train of packets in the log layer.

Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



Adrian, R. J. 1996 Stochastic estimation of the structure of turbulent fields. In Eddy Structure Identification (ed. Bonnet, J. P.), pp. 145196. Springer.CrossRefGoogle Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle Scholar
Adrian, R. J., Balachander, S. & Liu, Z.-C. 2001 Spanwise growth of vortex structure in wall turbulence. KSME Intl J. 15, 17411749.CrossRefGoogle Scholar
Adrian, R. J., Christensen, K. T. & Liu, Z.-C. 2000 b Analysis and interpretation of instantaneous turbulent velocity fields. Exp. Fluids 29, 275290.CrossRefGoogle Scholar
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 a Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.CrossRefGoogle Scholar
Balakumar, B. J. & Adrian, R. J. 2007 Large- and very-large-scale motions in channel and boundary-layer flows. Phil. Trans. R. Soc. Lond. A 365, 665681.Google ScholarPubMed
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433443.CrossRefGoogle Scholar
Chung, D. & Mckeon, B. J. 2010 Large-eddy simulation of large-scale structures in long channel flow. J. Fluid Mech. 661, 341364.CrossRefGoogle Scholar
Degraaff, D. B. & Eaton, J. K. 2000 Reynolds-number scaling of the flat-plate turbulent boundary layer. J. Fluid Mech. 422, 319346.CrossRefGoogle Scholar
Del Alamo, J. C. & Jimenez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor's approximation. J. Fluid Mech. 640, 526.CrossRefGoogle Scholar
Del Alamo, J. C., Jimenez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.CrossRefGoogle Scholar
Dennis, D. J. C. & Nickels, T. B. 2008 On the limitations of Taylor's hypothesis in constructing long structures in a turbulent boundary layer. J. Fluid Mech. 614, 197206.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Hambleton, W. T. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J. Fluid Mech. 524, 5780.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 3546.CrossRefGoogle Scholar
Guala, M., Hommema, S. E. & Adrian, R. J. 2006 Large-scale and very-large-scale motions in turbulent pipe flow. J. Fluid Mech. 554, 521542.CrossRefGoogle Scholar
Head, M. R. & Bbndyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297338.CrossRefGoogle 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, 2154.CrossRefGoogle Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 128.CrossRefGoogle Scholar
Jimenez, J. 1998. The largest scales of turbulent wall flows. Center for Turbulence Research, Annual Research Briefs, pp. 137154. Stanford University.Google Scholar
Khujadze, G. & Oberlack, M. 2004 DNS and scaling laws from new symmetry groups of ZPG turbulent boundary layer flow. Theor. Comput. Fluid Dyn. 18, 391411.CrossRefGoogle Scholar
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids 5, 695706.CrossRefGoogle 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, 125138.CrossRefGoogle Scholar
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417422.CrossRefGoogle Scholar
Krogstad, P. A., Kaspersen, J. H. & Rimestad, S. 1997 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids A 10, 949957.CrossRefGoogle Scholar
Lee, J. H. & Sung, H. J. 2011 Direct numerical simulation of a turbulent boundary layer up to Re θ = 2500. Intl J. Heat Fluid Flow 32, 110.CrossRefGoogle Scholar
Longmire, E. K., Ganapathisubramani, B. & Marusic, I. 2001 Structure identification and analysis in turbulent boundary layers by stereo PIV. In Proc. 4th Intl Symp. on Particle Image Velocimetry, 17–19 Sept., Gottingen, Germany.Google Scholar
Lund, T. S., Wu, X. & Squires, K. D. 1998 Generation of turbulent inflow data for spatially-developing boundary layer simulation. J. Comput. Phys. 140, 233258.CrossRefGoogle Scholar
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, 115130.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 b High Reynolds number effects in wall turbulence. Intl J. Heat Fluid Flow 31, 418428.CrossRefGoogle Scholar
Marusic, I., Mckeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 a Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22, 065103.CrossRefGoogle Scholar
Meinhart, C. D. & Adrian, R. J. 1995 On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7, 694696.CrossRefGoogle Scholar
Monty, J. P., Stewart, J. A., Williams, R. C. & Chong, M. S. 2007 Large-scale features in turbulent pipe and channel flows. J. Fluid Mech. 589, 147156.CrossRefGoogle Scholar
Priymak, V. G. & Miyazaki, T. 1994 Long-wave motions in turbulent shear flows. Phys. Fluids 6, 34543464.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motion in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.CrossRefGoogle Scholar
Schlatter, P., Örlü, R., Li, Q., Brethouwer, G., Fransson, J. H. M., Johansson, A. V., Alfredsson, P. H. & Henningson, D. S. 2009 Turbulent boundary layer up to Re θ = 2560 studied through simulation and experiment. Phys. Fluids 21, 051702.CrossRefGoogle Scholar
Simens, M. P., Jimenez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228, 42184231.CrossRefGoogle Scholar
Smith, C. R. 1984 A synthesized model of the near-wall behavior in turbulent boundary layers. In Proc. 8th Symp. on Turbulence (ed. Zakin, J. & Patterson, G.), pp. 299325. University of Missouri-Rolla.Google Scholar
Smith, C. R., Walker, J. D. A., Haidari, A. H. & Sobrun, U. 1991 On the dynamics of near-wall turbulence. Phil. Trans. R. Soc. Lond. A 336, 131175.Google Scholar
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to R θ = 1410. J. Fluid Mech. 187, 6198.CrossRefGoogle Scholar
Spalart, P. R., Coleman, G. N. & Johnstone, R. 2008 Retraction: ‘Direct numerical simulation of the Ekman layer: a step in Reynolds number, and cautious support for a log law with a shifted origin’. Phys. Fluids 21, 109901.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proc. 2nd Midwestern Conf. on Fluid Mech., pp. 119. Ohio State University, Columbus, Ohio.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.CrossRefGoogle Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Wark, C. E. & Nagib, H. M. 1989 Relation between outer structures and wall-layer events in boundary layers with and without manipulation. In Proc. 2nd IUTAM Symp. on Structure of Turbulence and Drag Reduction (ed. Gyr, A.), pp. 467474. Springer.Google Scholar
Wu, X. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 541.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 5576.CrossRefGoogle Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices. J. Fluid Mech. 387, 353396.CrossRefGoogle Scholar
Zhou, J., Meinhart, C. D., Balachandar, S. & Adrian, R. J. 1997 Formation of coherent hairpin packets in wall turbulence. In Self-Sustaining Mechanisms of Wall Turbulence (ed. Panton, R. L.), pp. 109134. Computational Mechanics, Southampton, UK.Google Scholar