Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-15T18:01:55.050Z Has data issue: false hasContentIssue false

Large-scale structures in turbulent and reverse-transitional sink flow boundary layers

Published online by Cambridge University Press:  13 April 2010

Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
Email address for correspondence:


Aspects of large-scale organized structures in sink flow turbulent and reverse-transitional boundary layers are studied experimentally using hot-wire anemometry. Each of the present sink flow boundary layers is in a state of ‘perfect equilibrium’ or ‘exact self-preservation’ in the sense of Townsend (The Structure of Turbulent Shear Flow, 1st and 2nd edns, 1956, 1976, Cambridge University Press) and Rotta (Progr. Aeronaut. Sci., vol. 2, 1962, pp. 1–220) and conforms to the notion of ‘pure wall-flow’ (Coles, J. Aerosp. Sci., vol. 24, 1957, pp. 495–506), at least for the turbulent cases. It is found that the characteristic inclination angle of the structure undergoes a systematic decrease with the increase in strength of the streamwise favourable pressure gradient. Detectable wall-normal extent of the structure is found to be typically half of the boundary layer thickness. Streamwise extent of the structure shows marked increase as the favourable pressure gradient is made progressively severe. Proposals for the typical eddy forms in sink flow turbulent and reverse-transitional flows are presented, and the possibility of structural self-organization (i.e. individual hairpin vortices forming streamwise coherent hairpin packets) in these flows is also discussed. It is further indicated that these structural ideas may be used to explain, from a structural viewpoint, the phenomenon of soft relaminarization or reverse transition of turbulent boundary layers when subjected to strong streamwise favourable pressure gradients. Taylor's ‘frozen turbulence’ hypothesis is experimentally shown to be valid for flows in the present study even though large streamwise accelerations are involved, the flow being even reverse transitional in some cases. Possible conditions, which are required to be satisfied for the safe use of Taylor's hypothesis in pressure-gradient-driven flows, are also outlined. Measured convection velocities are found to be fairly close to the local mean velocities (typically 90% or more) suggesting that the structure gets convected downstream almost along with the mean flow.

Copyright © Cambridge University Press 2010

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., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.CrossRefGoogle Scholar
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Large-scale motion of a turbulent boundary layer during relaminarization. J. Fluid Mech. 53, 6183.CrossRefGoogle Scholar
Bradshaw, P. & Wong, F. Y. F. 1972 The reattachment and relaxation of a turbulent shear layer. J. Fluid Mech. 52, 113135.CrossRefGoogle Scholar
Brown, G. L. & Thomas, A. S. W. 1977 Large structure in a turbulent boundary layer. Phys. Fluids 20 (10), S243S252.CrossRefGoogle Scholar
Chauhan, K. A., Nagib, H. M. & Monkewitz, P. A. 2007 Evidence on non-universality of Kármán constant. In Progress in Turbulence II: Proceedings of the iTi Conference in Turbulence 2005 (ed. Oberlack, M., Khujadze, G., Günther, S., Weller, T., Frewer, M., Peinke, J. & Barth, S.), Springer Proceedings in Physics, pp. 159163. Springer.CrossRefGoogle Scholar
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433443.CrossRefGoogle Scholar
Clauser, F. H. 1956 The turbulent boundary layer. Adv. Appl. Mech. 4, 151.CrossRefGoogle Scholar
Colella, K. J. & Keith, W. L. 2003 Measurements and scaling of wall shear stress fluctuations. Exp. Fluids 34, 253266.CrossRefGoogle Scholar
Coles, D. E. 1956 The law of the wake in the turbulent boundary layer. J. Fluid Mech. 1, 191226.CrossRefGoogle Scholar
Coles, D. E. 1957 Remarks on the equilibrium turbulent boundary layers. J. Aerosp. Sci. 24, 495506.Google 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
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
Dixit, S. A. & Ramesh, O. N. 2008 Pressure-gradient-dependent logarithmic laws in sink flow turbulent boundary layers. J. Fluid Mech. 615, 445475.CrossRefGoogle Scholar
Ganapathisubramani, B., Hutchins, N., Hambleton, W. T., Longmire, E. K. & 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
Head, M. R. 1976 Eddy viscosity in turbulent boundary layers. Aeronaut. Quart. 27, 270276.CrossRefGoogle Scholar
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297338.CrossRefGoogle Scholar
Hussain, A. K. M. F. 1983 Coherent structures – reality and myth. Phys. Fluids 26 (10), 28162850.CrossRefGoogle Scholar
Hutchins, N., Nickels, T. B., Marusic, I. & Chong, M. S. 2009 Hot-wire spatial resolution issues in wall-bounded turbulence. J. Fluid Mech. 635, 103136.CrossRefGoogle Scholar
Jones, M. B., Marusic, I. & Perry, A. E. 2001 Evolution and structure of sink-flow turbulent boundary layers. J. Fluid Mech. 428, 127.CrossRefGoogle Scholar
Krogstad, P.Å., Kaspersen, J. H. & Rimestad, S. 1998 Convection velocities in a turbulent boundary layer. Phys. Fluids 10 (4), 949957.CrossRefGoogle Scholar
Krogstad, P.Å. & Skåre, P. E. 1995 Influence of a strong adverse pressure gradient on the turbulent structure in a boundary layer. Phys. Fluids 7 (8), 20142024.CrossRefGoogle Scholar
Le, H., Moin, P. & Kim, J. 1997 Direct numerical simulation of turbulent flow over a backward-facing step. J. Fluid Mech. 330, 349374.CrossRefGoogle Scholar
Lee, J. H. & Sung, S. J. 2009 Structures in turbulent boundary layers subjected to adverse pressure gradients. J. Fluid Mech. 639, 101131.CrossRefGoogle Scholar
Ligrani, P. M. & Bradshaw, P. 1987 Spatial resolution and measurement of turbulence in the viscous sublayer using subminiature hot-wire probes. Exp. Fluids 5, 401417.CrossRefGoogle Scholar
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13 (3), 735743.CrossRefGoogle Scholar
Marusic, I. & Heuer, W. D. C. 2007 Reynolds number invariance of the structure inclination angle in wall turbulence. Phys. Rev. Lett. 99 (114504), 14.CrossRefGoogle ScholarPubMed
Marusic, I., Kunkel, G. J. & Porté-Agel, F. 2001 Experimental study of wall boundary conditions for large-eddy simulation. J. Fluid Mech. 446, 309320.CrossRefGoogle Scholar
Narasimha, R. 1983 Relaminarization – magnetohydrodynamic and otherwise. Progr. Astronaut. Aeronaut. 84, 3052.Google Scholar
Narasimha, R. & Sreenivasan, K. R. 1973 Relaminarization in highly accelerated turbulent boundary layers. J. Fluid Mech. 61, 417447.CrossRefGoogle Scholar
Narasimha, R. & Sreenivasan, K. R. 1979 Relaminarization of fluid flows. Adv. Appl. Mech. 19, 221309.CrossRefGoogle Scholar
Nickels, T. B. 2004 Inner scaling for wall-bounded flows subject to large pressure gradients. J. Fluid Mech. 521, 217239.CrossRefGoogle Scholar
Österlund, J. M. 1999 Experimental studies of zero pressure-gradient turbulent boundary layer flow. PhD thesis, Department of Mechanics, Royal Institute of Technology (KTH), Stockholm.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.CrossRefGoogle Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.CrossRefGoogle Scholar
Perry, A. E., Marusic, I. & Jones, M. B. 2002 On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients. J. Fluid Mech. 461, 6191.CrossRefGoogle Scholar
Perry, A. E., Marusic, I. & Li, J. D. 1994 Wall turbulence closure based on classical similarity laws and the attached eddy hypothesis. Phys. Fluids 6, 10241035.CrossRefGoogle Scholar
Piomelli, U., Ferziger, J., Moin, P. & Kim, J. 1989 New approximate boundary conditions for large eddy simulations of wall-bounded flows. Phys. Fluids A1 (6), 10611068.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.CrossRefGoogle Scholar
Rotta, J. C. 1962 Turbulent boundary layers in incompressible flow. Progr. Aeronaut. Sci. 2, 1220.CrossRefGoogle Scholar
Saddoughi, S. G. & Veeravalli, S. V. 1994 Local isotropy in turbulent boundary layers at high Reynolds number. J. Fluid Mech. 268, 333372.CrossRefGoogle Scholar
Schlichting, H. & Gersten, K. 2000 Boundary-Layer Theory, 8th edn. Springer.CrossRefGoogle Scholar
Spalart, P. R. & Leonard, A. 1987 Direct numerical simulation of equilibrium turbulent boundary layers. In Turbulent Shear Flows 5 (ed. Durst, F., Launder, B. E., Lumley, J. L., Schmidt, F. W. & Whitelaw, J. H.), pp. 234252. Springer.CrossRefGoogle Scholar
Sreenivasan, K. R. 1981 Relaminarizing flows (data evaluation). In The 1980-81 AFOSR-HTTM Stanford Conference on Complex Turbulent Flows: A Comparison of Computation and Experiment (ed. Cantwell, B. J., Kline, S. J. & Lilley, G. M.), vol. II, pp. 567581. Stanford University Press.Google Scholar
Sreenivasan, K. R. 1982 Laminarescent, relaminarizing and retransitional flows. Acta Mech. 44, 148.CrossRefGoogle Scholar
Taylor, G. I. 1938 The spectrum of turbulence. Proc. R. Soc. A 164, 476490.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT Press.CrossRefGoogle Scholar
Townsend, A. A. 1956 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear flow, 2nd edn. Cambridge University Press.Google Scholar
Uddin, A. K. M., Perry, A. E. & Marusic, I. 1997 On the validity of Taylor's hypothesis in wall turbulence. J. Mech. Engng Res. Dev. 19–20, 5766.Google Scholar
Wark, C. E. & Nagib, H. M. 1991 Experimental investigation of coherent structures in turbulent boundary layers. J. Fluid Mech. 230, 183208.CrossRefGoogle 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