Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-24T06:00:53.141Z Has data issue: false hasContentIssue false
  • English
  • Français

Analysis of vortex populations in turbulent wall-bounded flows

Published online by Cambridge University Press:  18 April 2011

Q. GAO ,
C. ORTIZ-DUEÑAS  and
E. K. LONGMIRE
Q. GAO
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
C. ORTIZ-DUEÑAS
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
E. K. LONGMIRE*
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
*
†Email address for correspondence: ellen@aem.umn.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

Vortical structures were identified and characterized using velocity fields of turbulent wall-bounded flows. Two direct numerical simulation data sets of fully developed channel flow at Reτ = 934 obtained by del Álamo et al. (J. Fluid Mech., vol. 500, 2004, p. 135) and Reτ = 590 obtained by Moser, Kim & Mansour (Phys. Fluids, vol. 11, 1999, p. 943) as well as dual-plane particle image velocimetry data at z+ = 110 in a zero-pressure-gradient turbulent boundary layer at Reτ = 1160 obtained by Ganapathisubramani, Longmire & Marusic (Phys. Fluids, vol. 18, 2006, 055105) were employed. The three-dimensional swirling strength based on the local velocity gradient tensor was employed to identify vortex core locations. The real eigenvector of the tensor was used both to refine the identification algorithm and to determine the orientation of each vortex core. The identification method allowed cores of nearly all orientations to be analysed. Circulation of each vortical structure was calculated using the vorticity vector projected onto the real eigenvector direction. Various population distributions were then computed at different wall-normal locations including core size, orientation, circulation and propagation velocity. The mean radius of the cores identified was found to increase with increasing wall-normal distance, and the mean circulation increases approximately quadratically with eddy radius. Orientations of cores with stronger circulation were distributed over a much narrower range than those for vortices with weaker circulation and were consistent with legs, necks and heads of forward-leaning hairpin structures.

JFM classification

Turbulent Flows: Turbulent boundary layers Boundary Layers: Boundary layer structure Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 678 , 10 July 2011 , pp. 87 - 123
Copyright
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.)

References

REFERENCES

Acarlar, M. S. & Smith, C. R. 1987 a A study of hairpin vortices in a laminar boundary layer. Part 1. Hairpin vortices generated by a hemisphere protuberance. J. Fluid Mech. 175, 1–41.CrossRefGoogle Scholar
Acarlar, M. S. & Smith, C. R. 1987 b A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection. J. Fluid Mech. 175, 43–83.CrossRefGoogle Scholar
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19, 041301.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle Scholar
Balint, J. L., Vukoslavcević, P. & Wallace, J. M. 1987 A study of the vortical structure of the turbulent boundary layer. In Advances in Turbulence (ed. Comte-Bellot, G. & Mathieu, J.), pp. 456–464. Springer-Verlag.CrossRefGoogle Scholar
Berdahl, C. H. & Thompson, D. S. 1993 Education of swirling structure using the velocity gradient tensor. AIAA J. 31, 97–103.CrossRefGoogle Scholar
Bernard, P. S., Thomas, J. M. & Handler, R. A. 1993 Vortex dynamics and the production of Reynolds stress. J. Fluid Mech. 253, 385–419.CrossRefGoogle Scholar
Carlier, J. & Stanislas, M. 2005 Experimental study of eddy structures in a turbulent boundary layer using particle image velocimetry. J. Fluid Mech. 535, 143–188.CrossRefGoogle Scholar
Chakraborty, P., Balachandar, S. & Adrian, R. J. 2005 On the relationships between local vortex identification schemes. J. Fluid Mech. 535, 189–214.CrossRefGoogle Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2, 765–777.CrossRefGoogle Scholar
Das, S. K., Tanahashi, M., Shoji, K. & Miyauchi, T. 2006 Statistical properties of coherent fine eddies in wall-bounded turbulent flow by direct numerical simulation. Theor. Comput. Fluid Dyn. 20 (2), 55–71.CrossRefGoogle Scholar
Elsinga, G. E., Adrian, R. J. & van Oudheusden, B. W. & Scarano, F. 2010 Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer. J. Fluid Mech. 644, 35–60.CrossRefGoogle Scholar
Elsinga, G. E., Scarano, F., Wieneke, B. & van Oudheusden, B. W. 2006 Tomographic particle image velocimetry. Exp. Fluids 41, 933–947.CrossRefGoogle Scholar
Falco, R. E. 1977 Coherent motions in the outer region of turbulent boundary layers. Phys. Fluids 20 (10), S124–S132.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Hambleton, W. T., Longmire, E. K. & Marusic, I. 2005 a Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations. J. Fluid Mech. 524, 57–80.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 35–46.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2006 Experimental investigation of vortex properties in a turbulent boundary layer. Phys. Fluids 18, 055105.CrossRefGoogle Scholar
Ganapathisubramani, B., Longmire, E. K., Marusic, I. & Pothos, S. 2005 b Dual-plane PIV technique to measure complete velocity gradient tensor in a turbulent boundary layer. Exp. Fluids 39, 222–231.CrossRefGoogle Scholar
Gao, Q., Ortiz-Dueñas, C. & Longmire, E. K. 2007 Circulation signature of vortical structures in turbulent boundary layers. In 16th Australasian Fluid Mechanics Conference. Gold Coast, Queensland, Australia.Google Scholar
Hambleton, W. T. 2007 Experimental study of coherent events in laminar and turbulent boundary layers. PhD thesis, University of Minnesota, Minneapolis.Google Scholar
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 53–64.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary layer structure. J. Fluid Mech. 107, 297–338.CrossRefGoogle Scholar
Hunt, J. C. R., Wray, A. A. & Moin, P. 1988 Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Rep. CTR-S88, pp. 193–208.Google Scholar
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.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.CrossRefGoogle Scholar
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335–360.CrossRefGoogle Scholar
Kim, J. 1987 Evolution of a vortical structure associated with the bursting event in a channel flow. In Turbulent Shear Flows, vol. 5, pp. 221–233. Springer-Verlag.CrossRefGoogle Scholar
Kim, K., Sung, H. J. & Adrian, R. J. 2008 Effects of background noise on generating coherent packets of hairpin vortices. Phys. Fluids 20, 105107.CrossRefGoogle Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13, 735–743.CrossRefGoogle Scholar
Moin, P. & Kim, J. 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations. J. Fluid Mech. 155, 441–461.CrossRefGoogle Scholar
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431–442.CrossRefGoogle Scholar
Moser, R. D., Kim, J. & Mansour, N. N. 1999 Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11 (4), 943–945.CrossRefGoogle Scholar
Natrajan, V. K., Wu, Y. & Christensen, K. T. 2007 Spatial signatures of retrograde spanwise vortices in wall turbulence. J. Fluid Mech. 574, 155–167.CrossRefGoogle Scholar
Ong, L. & Wallace, J. 1998 Joint probability density analysis of the structure and dynamics of the vorticity field of a turbulent boundary layer. J. Fluid Mech. 367, 291–328.CrossRefGoogle Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2008 Characterization of coherent vortical structures in a supersonic turbulent boundary layer. J. Fluid Mech. 613, 205–231.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Robinson, S. K. 1989 A review of vortex structures and associated coherent motions in turbulent boundary layers. In Proceedings of the Second IUTAM Symposium on Structure of Turbulence and Drag Reduction. Zurich, Switzerland.Google Scholar
Robinson, S. K. 1991 a Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601–639.CrossRefGoogle Scholar
Robinson, S. K. 1991 b The kinematics of turbulent boundary layer structures. NASA Tech. Memo. 103859.Google Scholar
Saikrishnan, N., Marusic, I. & Longmire, E. K. 2006 Assessment of dual plane PIV measurements in wall turbulence using DNS data. Exp. Fluids 41, 265–278.CrossRefGoogle Scholar
Schröder, A., Geisler, R., Elsinga, G. E., Scarano, F. & Dierksheide, U. 2008 Investigation of a turbulent spot and a tripped turbulent boundary layer flow using time-resolved tomographic PIV. Exp. Fluids 44, 305–316.CrossRefGoogle 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, 131–175.Google Scholar
Spina, E. F. & Smits, A. J. 1987 Organized structures in a compressible turbulent boundary layer. J. Fluid Mech. 182, 85–109.CrossRefGoogle Scholar
Stanislas, M., Perret, L. & Foucaut, J.-M. 2008 Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602, 327–382.CrossRefGoogle Scholar
Tanahashi, M., Kang, S.-J., Miyamoto, T., Shiokawa, S. & Miyauchi, T. 2004 Scaling law of fine scale eddies in turbulent channel. Intl J. Heat Fluid Flow 25, 331–340.CrossRefGoogle Scholar
Theodorsen, T. 1952 Mechanism of turbulence. In Proceedings of the Second Midwestern Conf. of Fluid Mechanics. Ohio State University, Columbus, OH.Google Scholar
Vukoslavcevic, P., Beratlis, N., Balaras, E., Wallace, J. M. & Sun, O. 2008 The velocity and vorticity vector fields of a turbulent boundary layer. Part 1. Simultaneous measurements by hot-wire anemometry. Exp. Fluids pp. 1432–1114.Google Scholar
Vukoslavcevic, P., Wallace, J. & Balint, J.-L. 1991 The velocity and vorticity vector fields of a turbulent boundary layer. Part 1. Simultaneous measurements by hot-wire anemometry. J. Fluid Mech. 228, 25–51.Google Scholar
Wallace, J. M. & Foss, J. 1995 The measurement of vorticity in turbulent flows. Annu. Rev. Fluid Mech. 27, 469–514.CrossRefGoogle Scholar
Wallace, J. M. & Vukoslavcevic, P. 2010 Measurement of the velocity gradient tensor in turbulent flows. Annu. Rev. Fluid Mech. 42, 157–181.CrossRefGoogle Scholar
Wu, X. Y. & Moin, P. 2009 Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41.CrossRefGoogle Scholar
Wu, Y. & Christensen, K. T. 2006 Population trends of spanwise vortices in wall turbulence. J. Fluid Mech. 568, 55–76.CrossRefGoogle Scholar
Zhou, J. 1997 Self-sustaining formation of packets of hairpin vortices in a turbulent wall layer. PhD thesis, University of Illinois, Urbana-Champaign.Google Scholar
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar