×

zbMATH — the first resource for mathematics

Vortex axis tracking by iterative propagation (VATIP): a method for analysing three-dimensional turbulent structures. (English) Zbl 1415.76377
Summary: Vortex is a central concept in the understanding of turbulent dynamics. Objective algorithms for the detection and extraction of vortex structures can facilitate the physical understanding of turbulence regeneration dynamics by enabling automated and quantitative analyses of these structures. Despite the wide availability of vortex identification criteria, they only label spatial regions belonging to vortices, without any information on the identity, topology and shape of individual vortices. This latter information is stored in the axis lines lining the contours of vortex tubes. In this study, a new tracking algorithm is proposed which propagates along the vortex axis lines and iteratively searches for new directions for growth. The method is validated in flow fields from transient simulations where vortices of different shapes are controllably generated. It is then applied to statistical turbulence for the analysis of vortex configurations and distributions. It is shown to reliably extract axis lines for complex three-dimensional vortices generated from the walls. A new procedure is also proposed that classifies vortices into commonly observed shapes, including quasi-streamwise vortices, hairpins, hooks and branches, based on their axis-line topology. Clustering analysis is performed on the extracted axis lines to reveal vortex organization patterns and their potential connection to large-scale motions in turbulence.
MSC:
76F40 Turbulent boundary layers
76M23 Vortex methods applied to problems in fluid mechanics
76F10 Shear flows and turbulence
76F65 Direct numerical and large eddy simulation of turbulence
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abe, H.; Kawamura, H.; Matsuo, Y., Direct numerical simulation of a fully developed turbulent channel flow with respect to the Reynolds number dependence, J. Fluid Mech., 123, 2, 382-393, (2001)
[2] Adrian, R. J., Stochastic estimation of conditional structure: a review, Appl. Sci. Res., 53, 3-4, 291-303, (1994) · Zbl 0823.76040
[3] Adrian, R. J., Hairpin vortex organization in wall turbulence a, Phys. Fluids, 19, 4, (2007) · Zbl 1146.76307
[4] Adrian, R. J.; Jones, B. G.; Chung, M. K.; Hassan, Y.; Nithianandan, C. K.; Tung, A. C., Approximation of turbulent conditional averages by stochastic estimation, Phys. Fluids A, 1, 6, 992-998, (1989)
[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] Bernard, P. S.; Thomas, J. M.; Handler, R. A., Vortex dynamics and the production of Reynolds stress, J. Fluid Mech., 253, 385-419, (1993) · Zbl 0800.76185
[7] Blackburn, H. M.; Mansour, N. N.; Cantwell, B. J., Topology of fine-scale motions in turbulent channel flow, J. Fluid Mech., 310, 269-292, (1996) · Zbl 0864.76036
[8] Blackwelder, R. F.; Kaplan, R. E., On the wall structure of the turbulent boundary layer, J. Fluid Mech., 76, 1, 89-112, (1976)
[9] Brandt, L.; Henningson, D. S., Transition of streamwise streaks in zero-pressure-gradient boundary layers, J. Fluid Mech., 472, 229-261, (2002) · Zbl 1163.76359
[10] Brandt, L.; De Lange, H. C., Streak interactions and breakdown in boundary layer flows, Phys. Fluids, 20, (2008) · Zbl 1182.76082
[11] Brooke, J. W.; Hanratty, T. J., Origin of turbulence-producing eddies in a channel flow, Phys. Fluids A, 5, 4, 1011-1022, (1993) · Zbl 0800.76195
[12] Cantwell, B. J., Organized motion in turbulent flow, Annu. Rev. Fluid Mech., 13, 1, 457-515, (1981)
[13] Chakraborty, P.; Balachandar, S.; Adrian, R. J., On the relationships between local vortex identification schemes, J. Fluid Mech., 535, 189-214, (2005) · Zbl 1071.76015
[14] Chen, Q.; Zhong, Q.; Qi, M.; Wang, X., Comparison of vortex identification criteria for planar velocity fields in wall turbulence, Phys. Fluids, 27, 8, (2015)
[15] Chong, M. S.; Perry, A. E.; Cantwell, B. J., A general classification of three-dimensional flow fields, Phys. Fluids A, 2, 5, 765-777, (1990)
[16] Chong, M. S.; Soria, J.; Perry, A. E.; Chacin, J.; Cantwell, B. J.; Na, Y., Turbulence structures of wall-bounded shear flows found using DNS data, J. Fluid Mech., 357, 225-247, (1998) · Zbl 0908.76039
[17] Corrsin, S.
[18] 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
[19] Dennis, D. J. C.; Nickels, T. B., Experimental measurement of large-scale three-dimensional structures in a turbulent boundary layer. Part 1. Vortex packets, J. Fluid Mech., 673, 180-217, (2011) · Zbl 1225.76009
[20] Dubief, Y.; Delcayre, F., On coherent-vortex identification in turbulence, J. Turbul., 1, 1-22, (2000) · Zbl 1082.76554
[21] Einstein, H. A.; Li, H., The viscous sublayer along a smooth boundary, J. Engng Mech. Div., 82, 2, 1-7, (1956)
[22] Ester, M.; Kriegel, H. P.; Sander, J.; Xu, X., A density-based algorithm for discovering clusters in large spatial databases with noise, Kdd, 96, 226-231, (1996), AAAI Press
[23] Gibson, J. F.
[24] Gibson, J. F.; Halcrow, J.; Cvitanotić, P., Equilibrium and travelling-wave solutions of plane Couette flow, J. Fluid Mech., 638, 243-266, (2009) · Zbl 1183.76688
[25] Hack, M. J. P.; Moin, P., Coherent instability in wall-bounded shear, J. Fluid Mech., 844, 917-955, (2018) · Zbl 1444.76060
[26] Haller, G., Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D, 149, 4, 248-277, (2001) · Zbl 1015.76077
[27] Haller, G., An objective definition of a vortex, J. Fluid Mech., 525, 1-26, (2005) · Zbl 1065.76031
[28] Haller, G., Lagrangian coherent structures, Annu. Rev. Fluid Mech., 47, 137-162, (2015)
[29] Hamilton, J. M.; Kim, J.; Waleffe, F., Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech., 287, 317-348, (1995) · Zbl 0867.76032
[30] Head, M. R.; Bandyopadhyay, P., New aspects of turbulent boundary-layer structure, J. Fluid Mech., 107, 297-338, (1981)
[31] Hinze, J. O., Turbulence, 223-225, (1975), McGraw-Gill
[32] Hoyas, S.; Jiménez, J., Scaling of the velocity fluctuations in turbulent channels up to Re_𝜏 = 2003, Phys. Fluids, 18, 1, (2006)
[33] Hunt, J. C. R.; Wray, A. A.; Moin, P., Eddies, streams, and convergence zones in turbulent flows, Proceedings of the 1988 Summer Program, Studying Turbulence Using Numerical Simulation Databases, 2, 193-208, (1988), Ames Research Center Stanford University
[34] Jeong, J.; Hussain, F., On the identification of a vortex, J. Fluid Mech., 285, 69-94, (1995) · Zbl 0847.76007
[35] Jeong, J.; Hussain, F.; Schoppa, W.; Kim, J., Coherent structures near the wall in a turbulent channel flow, J. Fluid Mech., 332, 185-214, (1997) · Zbl 0892.76036
[36] Jiménez, J., The largest scales of turbulent wall flows, CTR Annual Research Briefs, 137, 54, (1998), Stanford University
[37] Jiménez, J., Near-wall turbulence, Phys. Fluids, 25, 10, (2013)
[38] Jiménez, J., Coherent structures in wall-bounded turbulence, J. Fluid Mech., 842, P1, (2018)
[39] Jiménez, J.; Moin, P., The minimal flow unit in near-wall turbulence, J. Fluid Mech., 225, 213-240, (1991) · Zbl 0721.76040
[40] Jiménez, J.; Moser, R. D., What are we learning from simulating wall turbulence?, Phil. Trans. R. Soc. Lond. A, 365, 1852, 715-732, (2007) · Zbl 1152.76406
[41] Kida, S.; Miura, H., Identification and analysis of vortical structures, Eur. J Mech. (B/Fluids), 17, 4, 471-488, (1998) · Zbl 0921.76072
[42] Kim, H. T.; Kline, S. J.; Reynolds, W. C., The production of turbulence near a smooth wall in a turbulent boundary layer, J. Fluid Mech., 50, 1, 133-160, (1971)
[43] Kim, J.; Moin, P.; Moser, R., Turbulence statistics in fully-developed channel flow at low Reynolds-number, J. Fluid Mech., 177, 133-166, (1987) · Zbl 0616.76071
[44] Kim, K. C.; Adrian, R. J., Very large-scale motion in the outer layer, Phys. Fluids, 11, 2, 417-422, (1999) · Zbl 1147.76430
[45] Kline, S. J.; Reynolds, W. C.; Schraub, F. A.; Runstadler, P. W., The structure of turbulent boundary layers, J. Fluid Mech., 30, 4, 741-773, (1967)
[46] 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)
[47] Lozano-Durán, A.; Flores, O.; Jiménez, J., The three-dimensional structure of momentum transfer in turbulent channels, J. Fluid Mech., 694, 100-130, (2012) · Zbl 1250.76108
[48] Lozano-Durán, A.; Jiménez, J., Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades, J. Fluid Mech., 759, 432-471, (2014)
[49] Marusic, I.; Mckeon, B. J.; Monkewitz, P. A.; Nagib, H. M.; Smits, A. J.; Sreenivasan, K. R., Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues, Phys. Fluids, 22, 6, (2010) · Zbl 1190.76086
[50] Moisy, F.; Jiménez, J., Geometry and clustering of intense structures in isotropic turbulence, J. Fluid Mech., 513, 111-133, (2004) · Zbl 1107.76328
[51] Morris, S. C.; Stolpa, S. R.; Slaboch, P. E.; Klewicki, J. C., Near-surface particle image velocimetry measurements in a transitionally rough-wall atmospheric boundary layer, J. Fluid Mech., 580, 319-338, (2007) · Zbl 1113.76006
[52] Moser, R. D.; Kim, J.; Mansour, N. N., Direct numerical simulation of turbulent channel flow up to Re_𝜏 = 590, Phys. Fluids, 11, 4, 943-945, (1999) · Zbl 1147.76463
[53] Mullin, T., Experimental studies of transition to turbulence in a pipe, Annu. Rev. Fluid Mech., 43, 1-24, (2011) · Zbl 1210.76005
[54] 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)
[55] Panton, R. L., Overview of the self-sustaining mechanisms of wall turbulence, Prog. Aerosp. Sci., 37, 4, 341-383, (2001)
[56] Perry, A. E.; Chong, M. S., On the mechanism of wall turbulence, J. Fluid Mech., 119, 173-217, (1982) · Zbl 0517.76057
[57] Perry, A. E.; Marušić, 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
[58] Peyret, R., Spectral Methods for Incompressible Viscous Flow, (2002), Springer · Zbl 1005.76001
[59] Pope, S. B., Turbulent Flows, (2000), Cambridge University Press · Zbl 0966.76002
[60] Robinson, S. K., Coherent motions in the turbulent boundary layer, Annu. Rev. Fluid Mech., 23, 1, 601-639, (1991)
[61] Robinson, S. K.; Kline, S. J.; Spalart, P. R.
[62] Schlatter, P.; Brandt, L.; De Lange, H. C.; Henningson, D. S., On streak breakdown in bypass transition, Phys. Fluids, 20, (2008) · Zbl 1182.76669
[63] 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
[64] Schoppa, W.; Hussain, F., Coherent structure generation in near-wall turbulence, J. Fluid Mech., 453, 57-108, (2002) · Zbl 1141.76408
[65] Shekar, A.; Graham, M. D., Exact coherent states with hairpin-like vortex structure in channel flow, J. Fluid Mech., 849, 76-89, (2018) · Zbl 1415.76137
[66] Smith, C. R.
[67] Smith, C. R.; Schwartz, S. P., Observation of streamwise rotation in the near-wall region of a turbulent boundary layer, Phys. Fluids, 26, 3, 641-652, (1983)
[68] Theodorsen, T., Mechanism of turbulence, Proceedings of the Midwestern Conference on Fluid Mechanics, 1-19, (1952), Ohio State University
[69] Townsend, A. A. R., The Structure of Turbulent Shear Flow, (1980), Cambridge University Press · Zbl 0435.76033
[70] Tuckerman, L. S.; Kreilos, T.; Schrobsdorff, H.; Schneider, T. M.; Gibson, J. F., Turbulent-laminar patterns in plane Poiseuille flow, Phys. Fluids, 26, (2014)
[71] Waleffe, F., On a self-sustaining process in shear flows, Phys. Fluids, 9, 883-900, (1997)
[72] Waleffe, F., Three-dimensional coherent states in plane shear flows, Phys. Rev. Lett., 81, 4140-4143, (1998)
[73] Wallace, J. M.; Eckelmann, H.; Brodkey, R. S., The wall region in turbulent shear flow, J. Fluid Mech., 54, 1, 39-48, (1972)
[74] Willmarth, W. W.; Lu, S. S., Structure of the Reynolds stress near the wall, J. Fluid Mech., 55, 1, 65-92, (1972)
[75] Willmarth, W. W.; Tu, B. J., Structure of turbulence in the boundary layer near the wall, Phys. Fluids, 10, 9, S134-S137, (1967)
[76] 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
[77] Wu, X.; Moin, P.; Adrian, R. J.; Baltzer, J. R., Osborne Reynolds pipe flow: direct simulation from laminar through gradual transition to fully developed turbulence, Proc. Natl Acad. Sci. USA, 112, 7920-7924, (2015)
[78] Xi, L.; Bai, X., Marginal turbulent state of viscoelastic fluids: a polymer drag reduction perspective, Phys. Rev. E, 93, (2016)
[79] Xi, L.; Graham, M. D., Active and hibernating turbulence in minimal channel flow of Newtonian and polymeric fluids, Phys. Rev. Lett., 104, (2010)
[80] Xi, L.; Graham, M. D., Intermittent dynamics of turbulence hibernation in Newtonian and viscoelastic minimal channel flows, J. Fluid Mech., 693, 433-472, (2012) · Zbl 1250.76127
[81] Zhou, J.; Adrian, R. J.; Balachandar, S.; Kendall, T. M., Mechanisms for generating coherent packets of hairpin vortices in channel flow, J. Fluid Mech., 387, 353-396, (1999) · Zbl 0946.76030
[82] Zhu, L.; Schrobsdorff, H.; Schneider, T. M.; Xi, L., Distinct transition in flow statistics and vortex dynamics between low- and high-extent turbulent drag reduction in polymer fluids, J. Non-Newtonian Fluid Mech., 262, 115-130, (2018)
[83] Zhu, L.; Xi, L., Coherent structure dynamics and identification during the multistage transitions of polymeric turbulent channel flow, J. Phys.: Conf. Ser., 1001, 1, (2018)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.