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Uniform momentum zones in turbulent boundary layers. (English) Zbl 1381.76106
Summary: Structural properties of regions of uniform streamwise momentum in turbulent boundary layers are examined using experimental databases obtained from particle image velocimetry. This investigation employs a large range of Reynolds numbers, spanning more than an order of magnitude ($$Re_{\tau}=10^{3}{-}10^{4}$$), enabling us to provide a detailed description of uniform momentum zones as a function of Reynolds number. Our analysis starts by examining the identification criterion used by R. J. Adrian et al. [ibid. 422, 1–54 (2000; Zbl 0959.76503)] to report the presence of uniform momentum zones in turbulent boundary layers. This criterion is then applied to show that a zonal-like structural arrangement is prevalent in all datasets examined, emphasising its importance in the structural organisation. Streamwise velocity fluctuations within the zones are observed to be small but they are bounded by distinct step changes in streamwise momentum which indicate that shear layers of intense vorticity separate each zone. A log-linear increase in the number of these zones with increasing Reynolds number is revealed, together with an increase in the thicknesses of zones with increasing distance from the wall. These results support a hierarchical length-scale distribution of coherent structures, which generate zonal-like organisation within turbulent boundary layers. Interpretation of these findings is aided by employing synthetic velocity fields generated using a model based on the attached eddy hypothesis, which is described in the work of Perry and co-workers. Comparisons between the model and experimental results show that a hierarchy of self-similar structures leads to population densities and length-scale distributions of uniform momentum zones that closely adhere to those observed experimentally in this study.

##### MSC:
 76F40 Turbulent boundary layers
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##### References:
 [1] Acarlar, M. S.; Smith, C. R., A study of hairpin vortices in a laminar boundary. Part 1. Hairpin vortices generated by a hemisphere protuberance, J. Fluid Mech., 175, 1-41, (1987) [2] Acarlar, M. S.; Smith, C. R., A study of hairpin vortices in a laminar boundary layer. Part 2. Hairpin vortices generated by fluid injection, J. Fluid Mech., 175, 43-83, (1987) [3] Adrian, R. J., Hairpin vortex organization in wall turbulence, Phys. Fluids, 19, 4, (2007) · Zbl 1146.76307 [4] Adrian, R. J.; Marusic, I., Coherent structures in flow over hydraulic engineering surfaces, J. Hydraul Res., 50, 5, 451-464, (2012) [5] 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 [6] Adrian, R. J.; Westerweel, J., Particle Image Velocimetry, (2011), Cambridge University Press [7] Del Álamo, 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 [8] Del Álamo, J. C.; Jiménez, J.; Zandonade, P.; Moser, R. D., Self-similar vortex clusters in the turbulent logarithmic region, J. Fluid Mech., 561, 329-358, (2006) · Zbl 1157.76346 [9] Baltzer, J. R.; Adrian, R. J.; Wu, X., Structural organization of large and very large scales in turbulent pipe flow simulation, J. Fluid Mech., 720, 236-279, (2013) · Zbl 1284.76218 [10] Blackwelder, R. F.; Eckelmann, H., Streamwise vortices associated with the bursting phenomenon, J. Fluid Mech., 94, 3, 577-594, (1979) [11] 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) [12] 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 [13] Falco, R. E., Coherent motions in the outer region of turbulent boundary layers, Phys. Fluids, 20, S124-S132, (1977) [14] Ganapathisubramani, B.; Longmire, E. K.; Marusic, I., Characteristics of vortex packets in turbulent boundary layers, J. Fluid Mech., 478, 35-46, (2003) · Zbl 1032.76500 [15] 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 [16] Head, M. R.; Bandyopadhyay, P., New aspects of turbulent boundary-layer structure, J. Fluid Mech., 107, 297-338, (1981) [17] 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 [18] Hutchins, N.; Marusic, I., Evidence of very long meandering features in the logarithmic region of turbulent boundary layers, J. Fluid Mech., 579, 1-28, (2007) · Zbl 1113.76004 [19] Jiménez, J., Cascades in wall-bounded turbulence, Annu. Rev. Fluid Mech., 44, 27-45, (2012) · Zbl 1388.76089 [20] Kim, K. C.; Adrian, R. J., Very large-scale motion in the outer layer, Phys. Fluids, 11, 2, 417-422, (1999) · Zbl 1147.76430 [21] Klewicki, J. C., Reynolds number dependence, scaling, and dynamics of turbulent boundary layers, Trans. ASME J. Fluids Engng, 132, 9, (2010) [22] Klewicki, J.; Ebner, R.; Wu, X., Mean dynamics of transitional boundary-layer flow, J. Fluid. Mech., 682, 617-651, (2011) · Zbl 1241.76282 [23] Kline, S. J.; Reynolds, W. C.; Schraub, F. A.; Runstadler, P. W., The structure of turbulent boundary layers, J. Fluid Mech., 30, 741-773, (1967) [24] Kwon, Y. S.; Monty, J. P.; Philip, J.; De Silva, C. M.; Hutchins, N., The quiescent core of turbulent channel flow, J. Fluid Mech., 751, 228-254, (2014) · Zbl 1416.76063 [25] Lee, J.; Lee, J. H.; Choi, J.; Sung, H. J., Spatial organization of large- and very-large-scale motions in a turbulent channel flow, J. Fluid Mech., 749, 818-840, (2014) [26] Lee, J. H.; Sung, H. J., Very-large-scale motions in a turbulent boundary layer, J. Fluid Mech., 673, 80-120, (2011) · Zbl 1225.76162 [27] Marusic, I., On the role of large-scale structures in wall turbulence, Phys. Fluids, 13, 735-743, (2001) · Zbl 1184.76351 [28] Marusic, I., Unravelling turbulence near walls, J. Fluid Mech., 630, 1-4, (2009) · Zbl 1181.76083 [29] Marusic, I. & Adrian, R. J.2012The eddies and scales of wall turbulence. In Ten Chapters in Turbulence (ed. Davidson, P. A., Yukio, K. & Sreenivasan, K. R.). Cambridge University Press. · Zbl 1299.76086 [30] Marusic, I.; Monty, J. P.; Hultmark, M.; Smits, A. J., On the logarithmic region in wall turbulence, J. Fluid Mech., 716, R3, (2013) · Zbl 1284.76206 [31] Marusic, I.; Perry, A. E., A wall-wake model for the turbulence structure of boundary layers. Part 2. Further experimental support, J. Fluid Mech., 298, 389-407, (1995) [32] Meinhart, C. D.; Adrian, R. J., On the existence of uniform momentum zones in a turbulent boundary layer, Phy. Fluids, 7, 694, (1995) [33] Morrill-Winter, C.; Klewicki, J., Influences of boundary layer scale separation on the vorticity transport contribution to turbulent inertia, Phys. Fluids, 25, 1, 015108, (2013) [34] Na, Y.; Hanratty, T. J.; Liu, Z. C., The use of DNS to define stress producing events for turbulent flow over a smooth wall, Flow Turbul. Combust., 66, 4, 495-512, (2001) · Zbl 0993.76038 [35] Offen, G. R.; Kline, S. J., Combined dye-streak and hydrogen-bubble visual observations of a turbulent boundary layer, J. Fluid Mech., 62, 2, 223-239, (1974) [36] Offen, G. R.; Kline, S. J., A proposed model of the bursting process in turbulent boundary layers, J. Fluid Mech., 70, 2, 209-228, (1975) [37] Perry, A. E.; Chong, M. S., On the mechanism of wall turbulence, J. Fluid Mech., 119, 173-217, (1982) · Zbl 0517.76057 [38] Perry, A. E.; Henbest, S. M.; Chong, M., A theoretical and experimental study of wall turbulence, J. Fluid Mech., 165, 163-199, (1986) · Zbl 0597.76052 [39] Perry, A. E.; Marusic, I., A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis, J. Fluid Mech., 298, 361-388, (1995) · Zbl 0849.76030 [40] Philip, J.; Meneveau, C.; De Silva, C. M.; Marusic, I., Multiscale analysis of fluxes at the turbulent/non-turbulent interface in high Reynolds number boundary layers, Phys. Fluids, 26, 1, (2014) [41] 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 [42] Schlatter, P.; Li, Q.; Örlü, R.; Hussain, F.; Henningson, D. S., On the near-wall vortical structures at moderate Reynolds numbers, Eur. J. Mech. (B. Fluids), 48, 75-93, (2014) · Zbl 06931934 [43] Sillero, J. A.; Jiménez, J.; Moser, R. D., One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to $${\textit\delta}^{+}=2000$$, Phys. Fluids, 25, 10, (2013) [44] 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) [45] De Silva, C. M., Hutchins, N. & Marusic, I.2014bRegions of uniform streamwise momentum in turbulent boundary layers. In 19th Australasian Fluid Mechanics Conference. [46] De Silva, C. M.; Marusic, I.; Woodcock, J. D.; Meneveau, C., Scaling of second- and higher-order structure functions in turbulent boundary layers, J. Fluid Mech., 769, 654-686, (2015) [47] 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, 044501, (2013) [48] Smits, A. J.; Mckeon, B. J.; Marusic, I., High-Reynolds number wall turbulence, Annu. Rev. Fluid Mech., 43, 353-375, (2011) · Zbl 1299.76002 [49] Theodersen, T.1952Mechanism of turbulence. In Proc. Mid-west. Conf. Fluid Mech. [50] Tomkins, C. D.; Adrian, R. J., Spanwise structure and scale growth in turbulent boundary layers, J. Fluid Mech., 490, 1, 37-74, (2003) · Zbl 1063.76514 [51] Townsend, A. A., The Structure of Turbulent Shear Flow, (1976), Cambridge University Press · Zbl 0325.76063 [52] Wallace, J. M.; Eckelmann, H.; Brodkey, R. S., The wall region in turbulent shear flow, J. Fluid Mech., 54, 1, 39-48, (1972) [53] 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) [54] Woodcock, J. D.; Marusic, I., The statistical behaviour of attached eddies, Phys. Fluids, 27, 1, (2015) [55] Wu, X.; Moin, P., Direct numerical simulation of turbulence in a nominally-zero-pressure-gradient flat-plate boundary layer, J. Fluid Mech., 630, 5-41, (2009) · Zbl 1181.76084 [56] Zhou, J.; Adrian, R. J.; Balachandar, S.; Kendall, T., Mechanisms for generating coherent packets of hairpin vortices in channel flow, J. Fluid Mech., 387, 353-396, (1999) · Zbl 0946.76030
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