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Interfaces of uniform momentum zones in turbulent boundary layers. (English) Zbl 1383.76257
Summary: 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 (\(Re_{\tau}=10^{3}\)-\(10^{4}\)), 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.

76F40 Turbulent boundary layers
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[1] Adrian, R. J.; Meinhart, C. D.; Tomkins, C. D., Vortex organization in the outer region of the turbulent boundary layer, J. Fluid Mech., 422, 1-54, (2000) · Zbl 0959.76503
[2] Del Alamo, J. C.; Jiménez, J.; Zandonade, P.; Moser, R. D., Scaling of the energy spectra of turbulent channels, J. Fluid Mech., 500, 135-144, (2004) · Zbl 1059.76031
[3] Anand, R. K.; Boersma, B. J.; Agrawal, A., 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, 995-1007, (2009)
[4] Bisset, D. K.; Hunt, J. C. R.; Rogers, M. M., The turbulent/non-turbulent interface bounding a far wake, J. Fluid Mech., 451, 383-410, (2002) · Zbl 1156.76397
[5] Blackwelder, R. F.; Kovasznay, L. S. G., Time scales and correlations in a turbulent boundary layer, Phys. Fluids, 15, 1545-1554, (1972)
[6] Borrell, G.; Jiménez, J., Properties of the turbulent/non-turbulent interface in boundary layers, J. Fluid Mech., 801, 554-596, (2016)
[7] Brown, G. L.; Roshko, A., On density effects and large structure in turbulent mixing layers, J. Fluid Mech., 64, 4, 775-816, (1974) · Zbl 1416.76061
[8] Chauhan, K. A.; Monkewitz, P. A.; Nagib, H. M., Criteria for assessing experiments in zero pressure gradient boundary layers, Fluid Dyn. Res., 41, 2, (2009) · Zbl 1286.76007
[9] Chauhan, K.; Philip, J.; Marusic, I., Scaling of the turbulent/non-turbulent interface in boundary layers, J. Fluid Mech., 751, 298-328, (2014)
[10] Chauhan, K.; Philip, J.; De Silva, C. M.; Hutchins, N.; Marusic, I., The turbulent/non-turbulent interface and entrainment in a boundary layer, J. Fluid Mech., 742, 119-151, (2014)
[11] Christensen, K. T.; Adrian, R. J., Statistical evidence of hairpin vortex packets in wall turbulence, J. Fluid Mech., 431, 433-443, (2001) · Zbl 1008.76029
[12] Corrsin, S.; Kistler, A. L., Free-stream boundaries of turbulent flows, NACA Tech. Note, 1244, (1955)
[13] Eisma, J.; Westerweel, J.; Ooms, G.; Elsinga, G. E., Interfaces and internal layers in a turbulent boundary layer, Phys. Fluids, 27, 5, (2015)
[14] Hambleton, W. T.; Hutchins, N.; Marusic, I., Simultaneous orthogonal-plane particle image velocimetry measurements in a turbulent boundary layer, J. Fluid Mech., 560, 53-64, (2006) · Zbl 1122.76305
[15] Head, M. R.; Bandyopadhyay, P., New aspects of turbulent boundary-layer structure, J. Fluid Mech., 107, 297-338, (1981)
[16] Herpin, S.; Stanislas, M.; Foucaut, J. M.; Coudert, S., Influence of the Reynolds number on the vortical structures in the logarithmic region of turbulent boundary layers, J. Fluid Mech., 716, 5-50, (2013) · Zbl 1284.76204
[17] Heskestad, G., Hot-wire measurements in a plane turbulent jet, Trans. ASME J. Appl. Mech., 32, 4, 721-734, (1965)
[18] Holzner, M.; Lüthi, B., Laminar superlayer at the turbulence boundary, Phys. Rev. Lett., 106, 13, (2011)
[19] Ishihara, T.; Kaneda, Y.; Hunt, J. C. R., Thin shear layers in high Reynolds number turbulence - DNS results, Flow Turbul. Combust., 91, 4, 895-929, (2013)
[20] Ishihara, T.; Ogasawara, H.; Hunt, J. C. R., Analysis of conditional statistics obtained near the turbulent/non-turbulent interface of turbulent boundary layers, J. Fluids Struct., 53, 50-57, (2015)
[21] Jiménez, J.; Hoyas, S.; Simens, M. P.; Mizuno, Y., Turbulent boundary layers and channels at moderate Reynolds numbers, J. Fluid Mech., 657, 335-360, (2010) · Zbl 1197.76063
[22] Krug, D.; Philip, J.; Marusic, I., Uniform momentum zones in turbulent boundary layers, J. Fluid Mech., 811, 421-435, (2017) · Zbl 1383.76235
[23] Kwon, Y. S.; Philip, J.; De Silva, C. M.; Monty, N.; Hutchins, J. P., The quiescent core of turbulent channel flow, J. Fluid Mech., 751, 228-254, (2014) · Zbl 1416.76063
[24] Mandelbrot, B. B., The Fractal Geometry of Nature, (1982), W. H. Freeman · Zbl 0504.28001
[25] Mathew, J.; Basu, A. J., Some characteristics of entrainment at a cylindrical turbulence boundary, Phys. Fluids, 14, 7, 2065-2072, (2002) · Zbl 1185.76246
[26] Meinhart, C. D.; Adrian, R. J., On the existence of uniform momentum zones in a turbulent boundary layer, Phys. Fluids, 7, 694, (1995)
[27] Meneveau, C.; Sreenivasan, K. R., Interface dimension in intermittent turbulence, Phys. Rev. A, 41, 4, 2246, (1990)
[28] Miller, P. L.; Dimotakis, P. E., Stochastic geometric properties of scalar interfaces in turbulent jets, Phys. Fluids A, 3, 1, 168-177, (1991)
[29] Mistry, D.; Philip, J.; Dawson, J. R.; Marusic, I., Entrainment at multi-scales across the turbulent/nonturbulent interface in an axisymmetric jet, J. Fluid Mech., 802, 690-725, (2016)
[30] Morrill-Winter, C.; Klewicki, J., Influences of boundary layer scale separation on the vorticity transport contribution to turbulent inertia, Phys. Fluids, 25, 1, (2013)
[31] Perry, A. E.; Chong, M. S., On the mechanism of wall turbulence, J. Fluid Mech., 119, 173, 106-121, (1982) · Zbl 0517.76057
[32] Philip, J.; Marusic, I., Large-scale eddies and their role in entrainment in turbulent jets and wakes, Phys. Fluids, 24, 5, (2012)
[33] Prasad, R. R.; Sreenivasan, K. R., Scalar interfaces in digital images of turbulent flows, Exp. Fluids, 7, 4, 259-264, (1989)
[34] Priyadarshana, P. J. A.; Klewicki, J. C.; Treat, S.; Foss, J. F., Statistical structure of turbulent-boundary-layer velocity – vorticity products at high and low Reynolds numbers, J. Fluid Mech., 570, 307-346, (2007) · Zbl 1106.76317
[35] Robinson, S. K., Coherent motions in the turbulent boundary layer, Annu. Rev. Fluid Mech., 23, 1, 601-639, (1991)
[36] Semin, N.; Golub, V.; Elsinga, G.; Westerweel, J., Laminar superlayer in a turbulent boundary layer, Tech. Phys. Lett., 37, 12, 1154-1157, (2011)
[37] Siebesma, A. P.; Jonker, H. J. J., Anomalous scaling of cumulus cloud boundaries, Phys. Rev. Lett., 85, 1, 214-217, (2000)
[38] Sillero, J. A.; Jiménez, J.; Moser, R. D., One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to 𝛿+ = 2000, Phys. Fluids, 25, 10, (2013)
[39] Da Silva, C. B.; Hunt, J. C. R.; Eames, I.; Westerweel, J., Interfacial layers between regions of different turbulence intensity, Annu. Rev. Fluid Mech., 46, 567-590, (2014) · Zbl 1297.76074
[40] Da Silva, C. B.; Taveira, R. R., 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, (2010)
[41] De Silva, C. M., Chauhan, K. A., Atkinson, C. H., Buchmann, N. A., Hutchins, N., Soria, J. & Marusic, I.2015Implementation of large scale PIV measurements for wall bounded turbulence at high Reynolds numbers. In 18th Australasian Fluid Mechanics Conference, Australian Fluid Mechanics Society.
[42] De Silva, C. M.; Gnanamanickam, E. P.; Atkinson, C.; Buchmann, N. A.; Hutchins, N.; Soria, J.; Marusic, I., High spatial range velocity measurements in a high Reynolds number turbulent boundary layer, Phys. Fluids, 26, 2, (2014)
[43] De Silva, C. M.; Hutchins, N.; Marusic, I., Uniform momentum zones in turbulent boundary layers, J. Fluid Mech., 786, 309-331, (2016) · Zbl 1381.76106
[44] De Silva, C. M.; Philip, J.; Chauhan, K.; Meneveau, C.; Marusic, I., Multiscale geometry and scaling of the turbulent-nonturbulent interface in high Reynolds number boundary layers, Phys. Rev. Lett., 111, (2013)
[45] De Silva, C. M., Squire, D. T., Hutchins, N. & Marusic, I.2012Towards 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. 1-4. University of Melbourne.
[46] Sreenivasan, K. R.; Meneveau, C., The fractal facets of turbulence, J. Fluid Mech., 173, 1, 357-386, (1986)
[47] Sreenivasan, K. R.; Ramshankar, R.; Meneveau, C., Mixing, entrainment and fractal dimensions of surfaces in turbulent flows, Proc. R. Soc. Lond. A, 421, 1860, 79-108, (1989) · Zbl 0674.76039
[48] Tennekes, H.; Lumley, J. L., A First Course in Turbulence, (1972), MIT · Zbl 0285.76018
[49] Townsend, A. A., The Structure of Turbulent Shear Flow, (1976), Cambridge University Press · Zbl 0325.76063
[50] Westerweel, J.; Fukushima, C.; Pedersen, J. M.; Hunt, J. C. R., Mechanics of the turbulent-nonturbulent interface of a jet, Phys. Rev. Lett., 95, (2005)
[51] Westerweel, J.; Fukushima, C.; Pedersen, J. M.; Hunt, J. C. R., Momentum and scalar transport at the turbulent/non-turbulent interface of a jet, J. Fluid Mech., 631, 199-230, (2009) · Zbl 1181.76015
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