Skip to main content

Interfaces of uniform momentum zones in turbulent boundary layers

  • Charitha M. de Silva (a1), Jimmy Philip (a1), Nicholas Hutchins (a1) and Ivan Marusic (a1)

In this paper we examine the characteristics of the interfaces that demarcate regions of relatively uniform streamwise momentum in turbulent boundary layers. The analysis utilises particle image velocimetry databases that span more than an order of magnitude of friction Reynolds number ( $Re_{\unicode[STIX]{x1D70F}}=10^{3}$ $10^{4}$ ), enabling us to provide a detailed description of the interfacial layers as a function of Reynolds number. As reported by Adrian et al. (J. Fluid Mech., vol. 422, 2000, pp. 1–54), these interfaces appear as persistent regions of strong shear with distinct patches of vorticity consistent with a packet-like structure. Here, however, we treat these interfaces as continuous lines, thus averaging the properties of the vortical patches, and find that their geometry is highly contorted and exhibits self-similarity across a wide range of scales. Specifically, the lengths of the edges of uniform momentum zones exhibit a power-law behaviour with a fractal scaling that has a constant exponent across the boundary layer, while the topmost edge or the turbulent/non-turbulent interface shows a sudden increase in the exponent. The accompanying sharp changes in velocity that occur at these edges are found to change in magnitude as a function of wall-normal height, being larger closer to the wall. Further, a Reynolds number invariance is exhibited when the magnitude of the step-like changes in velocity is scaled by the skin-friction velocity, meanwhile, the width across which it occurs is shown to be of the order of the Taylor microscale. Based on these quantitative measures, the Reynolds number scaling observed and the persistent presence of sharp changes in momentum in turbulent boundary layers, a simple model is used to reconstruct the mean velocity profile. Insight gained from the model enhances our understanding of how instantaneous phenomena (such as a zonal-like structural arrangement) manifests in the averaged flow statistics and confirms that the instantaneous momentum in a turbulent boundary layer appears to mainly consist of a step-like profile as a function of wall-normal distance.

Corresponding author
Email address for correspondence:
Hide All
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.
del Alamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
Anand, R. K., Boersma, B. J. & Agrawal, A. 2009 Detection of turbulent/non-turbulent interface for an axisymmetric turbulent jet: evaluation of known criteria and proposal of a new criterion. Exp. Fluids 47 (6), 9951007.
Bisset, D. K., Hunt, J. C. R. & Rogers, M. M. 2002 The turbulent/non-turbulent interface bounding a far wake. J. Fluid Mech. 451, 383410.
Blackwelder, R. F. & Kovasznay, L. S. G. 1972 Time scales and correlations in a turbulent boundary layer. Phys. Fluids 15, 15451554.
Borrell, G. & Jiménez, J. 2016 Properties of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 801, 554596.
Brown, G. L. & Roshko, A. 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (4), 775816.
Chauhan, K. A., Monkewitz, P. A. & Nagib, H. M. 2009 Criteria for assessing experiments in zero pressure gradient boundary layers. Fluid Dyn. Res. 41 (2), 021404.
Chauhan, K., Philip, J. & Marusic, I. 2014a Scaling of the turbulent/non-turbulent interface in boundary layers. J. Fluid Mech. 751, 298328.
Chauhan, K., Philip, J., de Silva, C. M., Hutchins, N. & Marusic, I. 2014b The turbulent/non-turbulent interface and entrainment in a boundary layer. J. Fluid Mech. 742, 119151.
Christensen, K. T. & Adrian, R. J. 2001 Statistical evidence of hairpin vortex packets in wall turbulence. J. Fluid Mech. 431, 433443.
Corrsin, S. & Kistler, A. L. 1955 Free-stream boundaries of turbulent flows. NACA Tech. Note 1244.
Eisma, J., Westerweel, J., Ooms, G. & Elsinga, G. E. 2015 Interfaces and internal layers in a turbulent boundary layer. Phys. Fluids 27 (5), 055103.
Hambleton, W. T., Hutchins, N. & Marusic, I. 2006 Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer. J. Fluid Mech. 560, 5364.
Head, M. R. & Bandyopadhyay, P. 1981 New aspects of turbulent boundary-layer structure. J. Fluid Mech. 107, 297338.
Herpin, S., Stanislas, M., Foucaut, J. M. & Coudert, S. 2013 Influence of the Reynolds number on the vortical structures in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 716, 550.
Heskestad, G. 1965 Hot-wire measurements in a plane turbulent jet. Trans. ASME J. Appl. Mech. 32 (4), 721734.
Holzner, M. & Lüthi, B. 2011 Laminar superlayer at the turbulence boundary. Phys. Rev. Lett. 106 (13), 134503.
Ishihara, T., Kaneda, Y. & Hunt, J. C. R. 2013 Thin shear layers in high Reynolds number turbulence – DNS results. Flow Turbul. Combust. 91 (4), 895929.
Ishihara, T., Ogasawara, H. & Hunt, J. C. R. 2015 Analysis of conditional statistics obtained near the turbulent/non-turbulent interface of turbulent boundary layers. J. Fluids Struct. 53, 5057.
Jiménez, J., Hoyas, S., Simens, M. P. & Mizuno, Y. 2010 Turbulent boundary layers and channels at moderate Reynolds numbers. J. Fluid Mech. 657, 335360.
Krug, D., philip, J. & Marusic, I. 2017 Uniform momentum zones in turbulent boundary layers. J. Fluid Mech. 811, 421435.
Kwon, Y. S., Philip, J., de Silva, C. M., Monty, N. & Hutchins, J. P. 2014 The quiescent core of turbulent channel flow. J. Fluid Mech. 751, 228254.
Mandelbrot, B. B. 1982 The Fractal Geometry of Nature. W. H. Freeman.
Mathew, J. & Basu, A. J. 2002 Some characteristics of entrainment at a cylindrical turbulence boundary. Phys. Fluids 14 (7), 20652072.
Meinhart, C. D. & Adrian, R. J. 1995 On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids 7, 694.
Meneveau, C. & Sreenivasan, K. R. 1990 Interface dimension in intermittent turbulence. Phys. Rev. A 41 (4), 2246.
Miller, P. L. & Dimotakis, P. E. 1991 Stochastic geometric properties of scalar interfaces in turbulent jets. Phys. Fluids A 3 (1), 168177.
Mistry, D., Philip, J., Dawson, J. R. & Marusic, I. 2016 Entrainment at multi-scales across the turbulent/nonturbulent interface in an axisymmetric jet. J. Fluid Mech. 802, 690725.
Morrill-Winter, C. & Klewicki, J. 2013 Influences of boundary layer scale separation on the vorticity transport contribution to turbulent inertia. Phys. Fluids 25 (1), 015108.
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119 (173), 106121.
Philip, J. & Marusic, I. 2012 Large-scale eddies and their role in entrainment in turbulent jets and wakes. Phys. Fluids 24 (5), 055108.
Prasad, R. R. & Sreenivasan, K. R. 1989 Scalar interfaces in digital images of turbulent flows. Exp. Fluids 7 (4), 259264.
Priyadarshana, P. J. A., Klewicki, J. C., Treat, S. & Foss, J. F. 2007 Statistical structure of turbulent-boundary-layer velocity–vorticity products at high and low Reynolds numbers. J. Fluid Mech. 570, 307346.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601639.
Semin, N., Golub, V., Elsinga, G. & Westerweel, J. 2011 Laminar superlayer in a turbulent boundary layer. Tech. Phys. Lett. 37 (12), 11541157.
Siebesma, A. P. & Jonker, H. J. J. 2000 Anomalous scaling of cumulus cloud boundaries. Phys. Rev. Lett. 85 (1), 214217.
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.
da Silva, C. B., Hunt, J. C. R., Eames, I. & Westerweel, J. 2014 Interfacial layers between regions of different turbulence intensity. Annu. Rev. Fluid Mech. 46, 567590.
da Silva, C. B. & Taveira, R. R. 2010 The thickness of the turbulent/nonturbulent interface is equal to the radius of the large vorticity structures near the edge of the shear layer. Phys. Fluids 22 (12), 121702.
de Silva, C. M., Chauhan, K. A., Atkinson, C. H., Buchmann, N. A., Hutchins, N., Soria, J. & Marusic, I. 2015 Implementation of large scale PIV measurements for wall bounded turbulence at high Reynolds numbers. In 18th Australasian Fluid Mechanics Conference, Australian Fluid Mechanics Society.
de Silva, C. M., Gnanamanickam, E. P., Atkinson, C., Buchmann, N. A., Hutchins, N., Soria, J. & Marusic, I. 2014 High spatial range velocity measurements in a high Reynolds number turbulent boundary layer. Phys. Fluids 26 (2), 025117.
de Silva, C. M., Hutchins, N. & Marusic, I. 2016 Uniform momentum zones in turbulent boundary layers. J. Fluid Mech. 786, 309331.
de Silva, C. M., Philip, J., Chauhan, K., Meneveau, C. & Marusic, I. 2013 Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers. Phys. Rev. Lett. 111, 044501.
de Silva, C. M., Squire, D. T., Hutchins, N. & Marusic, I. 2012 Towards capturing large scale coherent structures in boundary layers using particle image velocimetry. In Proceedings of the 6th Australian Conference on Laser Diagnostics in Fluid Mechanics and Combustion, pp. 14. University of Melbourne.
Sreenivasan, K. R. & Meneveau, C. 1986 The fractal facets of turbulence. J. Fluid Mech. 173 (1), 357386.
Sreenivasan, K. R., Ramshankar, R. & Meneveau, C. 1989 Mixing, entrainment and fractal dimensions of surfaces in turbulent flows. Proc. R. Soc. Lond. A 421 (1860), 79108.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2005 Mechanics of the turbulent-nonturbulent interface of a jet. Phys. Rev. Lett. 95, 174501.
Westerweel, J., Fukushima, C., Pedersen, J. M. & Hunt, J. C. R. 2009 Momentum and scalar transport at the turbulent/non-turbulent interface of a jet. J. Fluid Mech. 631, 199230.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *

JFM classification


Full text views

Total number of HTML views: 5
Total number of PDF views: 287 *
Loading metrics...

Abstract views

Total abstract views: 454 *
Loading metrics...

* Views captured on Cambridge Core between 12th May 2017 - 17th August 2018. This data will be updated every 24 hours.