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Evolution of material surfaces in the temporal transition in channel flow. (English) Zbl 1382.76132
Summary: We report a Lagrangian study on the evolution of material surfaces in the Klebanoff-type temporal transitional channel flow. Based on the Eulerian velocity field from the direct numerical simulation, a backward-particle-tracking method is applied to solve the transport equation of the Lagrangian scalar field, and then the isosurfaces of the Lagrangian field can be extracted as material surfaces in the evolution. Three critical issues for Lagrangian investigations on the evolution of coherent structures using material surfaces are addressed. First, the initial scalar field is uniquely determined based on the proposed criteria, so that the initial material surfaces can be approximated as vortex surfaces, and remain invariant in the initial laminar state. Second, the evolution of typical material surfaces initially from different wall distances is presented, and then the influential material surface with the maximum deformation is identified. Large vorticity variations with the maximum curvature growth of vortex lines are also observed on this surface. Moreover, crucial events in the transition can be characterized in a Lagrangian approach by conditional statistics on the material surfaces. Finally, the influential material surface, which is initially a vortex surface, is demonstrated as a surrogate of the vortex surface before significant topological changes of vortical structures. Therefore, this material surface can be used to elucidate the continuous temporal evolution of vortical structures in transitional wall-bounded flows in a Lagrangian perspective. The evolution of the influential material surface is divided into three stages: the formation of a triangular bulge from an initially disturbed streamwise–spanwise sheet, rolling up of the vortex sheet near the bulge ridges with the vorticity intensification and the generation and evolution of signature hairpin-like structures with self-induced dynamics of vortex filaments.

76F40 Turbulent boundary layers
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76F06 Transition to turbulence
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[1] Adrian, R. J., Hairpin vortex organization in wall turbulence, Phys. Fluids, 19, (2007) · Zbl 1146.76307
[2] Bake, S.; Fernholz, H. H.; Kachanov, Y. S., Resemblance of K- and N-regimes of boundary-layer transition at late stages, Eur. J. Mech. (B/Fluids), 19, 1-22, (2000) · Zbl 0953.76502
[3] Bake, S.; Meyer, D. G. W.; Rist, U., Turbulence mechanism in Klebanoff transition: a quantitative comparison of experiment and direct numerical simulation, J. Fluid Mech., 459, 217-243, (2002) · Zbl 0991.76512
[4] Batchelor, G. K., Introduction to Fluid Dynamics, (1967), Cambridge University Press · Zbl 0152.44402
[5] Bernard, P. S., The hairpin vortex illusion, J. Phys.: Conf. Ser., 318, (2011)
[6] Bernard, P. S., Vortex dynamics in transitional and turbulent boundary layers, AIAA J., 51, 1828-1842, (2013)
[7] Blazevski, D.; Haller, G., Hyperbolic and elliptic transport barriers in three-dimensional unsteady flows, Physica D, 273, 46-62, (2014) · Zbl 1341.37014
[8] Borodulin, V. I.; Gaponenko, V. R.; Kachanov, Y. S.; Meyer, D. G. W.; Rist, U.; Lian, Q. X.; Lee, C. B., Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment, Theor. Comput. Fluid Dyn., 15, 317-337, (2002) · Zbl 1057.76529
[9] Borodulin, V. I.; Kachanov, Y. S., Role of the mechanism of local secondary instability in K-breakdown of boundary layer, Izv. Sib. Otd. Akad. Nauk SSSR, Ser. Tekh. Nauk, 18, 65-77, (1988)
[10] Borodulin, V. I.; Kachanov, Y. S.; Koptsev, D. B., Experimental study of resonant interactions of instability waves in a self-similar boundary layer with an adverse pressure gradient: I. Tuned resonances, J. Turbul., 3, 1-38, (2002)
[11] Borodulin, V. I.; Kachanov, Y. S.; Roschektayev, A. P., Turbulence production in an APG-boundary-layer transition induced by randomized perturbations, J. Turbul., 7, 1-30, (2006)
[12] Borodulin, V. I., Kachanov, Y. S. & Roschektayev, A. P.2007The deterministic wall turbulence is possible. In Advances in Turbulence XI. Proceedings of 11th EUROMECH European Turbulence Conference (ed. Palma, J. M. L. M. & Lopes, A. S.), pp. 176-178. Springer. doi:10.1007/978-3-540-72604-3_55
[13] Brethouwer, G.; Hunt, J. C. R.; Nieuwstadt, F. T. M., Micro-structure and Lagrangian statistics of the scalar field with a mean gradient in isotropic turbulence, J. Fluid Mech., 474, 193-225, (2003) · Zbl 1065.76110
[14] Canuto, C.; Hussaini, M. Y.; Quateroni, A.; Zang, T. A., Spectral Methods in Fluid Dynamics, (1988), Springer
[15] Carino, E. R.; Brodkey, R. S., A visual investigation of the wall region in turbulent flow, J. Fluid Mech., 37, 1-30, (1969)
[16] Chong, M. S.; Perry, A. E.; Cantwell, B. J., A general classification of three-dimensional flow fields, Phys. Fluids A, 2, 765-777, (1990)
[17] Crow, S. C., Stability theory for a pair of trailing vortices, AIAA J., 8, 2172-2179, (1970)
[18] Fasel, H., Thumm, A. & Bestek, H.1993Direct numerical simulation of transition in supersonic boundary layers: oblique breakdown. In Transition and Turbulent Compressible Flows (ed. Kral, L. D. & Zang, T. A.), pp. 77-92. ASME.
[19] Gilbert, N. & Kleiser, L.1990Near-wall phenomena in transition to turbulence. In Near Wall Turbulence (ed. Kline, S. J. & Afgan, N. H.), pp. 7-27. Hemisphere.
[20] Green, M. A.; Rowley, C. W.; Haller, G., Detection of Lagrangian coherent structures in three-dimensional turbulence, J. Fluid Mech., 572, 111-120, (2007) · Zbl 1111.76025
[21] Guo, H.; Borodulin, V. I.; Kachanov, Y. S.; Pan, C.; Wang, J. J.; Lian, Q. X.; Wang, S. F., Nature of sweep and ejection events in transitional and turbulent boundary layers, J. Turbul., 11, 1-51, (2010)
[22] Haller, G., Distinguished material surfaces and coherent structures in three-dimensional fluid flows, Physica D, 149, 248-277, (2001) · Zbl 1015.76077
[23] Haller, G., Lagrangian coherent structures, Annu. Rev. Fluid Mech., 47, 137-162, (2015)
[24] Hama, F. R.1960Boundary-layer transition induced by a vibrating ribbon on a flat plate. In Proc. Heat Transfer and Fluid Mech. Inst. (ed. Roshko, A., Sturtevant, B. & Bartz, D. R.), pp. 92-105. Standford University Press.
[25] Hama, F. R. & Nutant, J.1963Detailed flow-field observations in the transition process in a thick boundary layer. In Proc. Heat Transfer and Fluid Mech. Inst., pp. 77-93. Standford University Press. · Zbl 0114.41802
[26] Head, M. R.; Bandyopadhyay, P., New aspects of turbulent boundary-layer structure, J. Fluid Mech., 107, 297-338, (1981)
[27] Herbert, T.1984 Analysis of the subharmonic route to transition in boundary-layers. AIAA Paper 84-0009.
[28] Herbert, T., Secondary instability of boundary layers, Annu. Rev. Fluid Mech., 20, 487-526, (1988)
[29] Hunt, J. C. R., Wray, A. A. & Moin, P.1988Eddies, stream, and convergence zones in turbulent flows. In Studying Turbulence Using Numerical Simulation Databases, 2, vol. 1, pp. 193-208. Center for Turbulence Research Report CTR-S88.
[30] Jeong, J.; Hussain, F., On the identification of a vortex, J. Fluid Mech., 285, 69-94, (1995) · Zbl 0847.76007
[31] Kachanov, Y. S., Physical mechanism of laminar-boundary-layer transition, Annu. Rev. Fluid Mech., 26, 411-482, (1994)
[32] Kachanov, Y. S.; Kozlov, V. V.; Levchenko, V. Y., Nonlinear development of a wave in a boundary layer, Fluid Dyn., 12, 383-390, (1977)
[33] Kim, J.; Moin, P., The structure of the vorticity field in turbulent channel flow. Part 2. Study of ensemble-averaged fields, J. Fluid Mech., 162, 339-363, (1986)
[34] Kim, J.; Moin, P.; Moser, R. D., Turbulent statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 177, 133-166, (1987) · Zbl 0616.76071
[35] Klebanoff, P. S.; Tidstrom, K. D.; Sargent, L. M., The three-dimensional nature of boundary-layer instability, J. Fluid Mech., 12, 1-34, (1962) · Zbl 0131.41901
[36] Kleiser, L. & Laurien, E.1985Three-dimensional numerical simulation of laminar – turbulent transition and its control by periodic disturbances. In Laminar-Turbulent Transition (ed. Kozlov, V. V.), pp. 29-37. Springer.
[37] Kleiser, L.; Zang, T. A., Numerical simulation of transition in wall-bounded shear flows, Annu. Rev. Fluid Mech., 23, 495-537, (1991)
[38] Lee, C. B.; Li, R., Dominant structure for turbulent production in a transitional boundary layer, J. Turbul., 8, 1-34, (2007)
[39] Lee, C. B.; Wu, J. Z., Transition in wall-bounded flows, Appl. Mech. Rev., 61, (2008) · Zbl 1146.76601
[40] Lehew, J. A.; Guala, M.; Mekeon, B. J., Time-resolved measurements of coherent structures in the turbulent boundary layer, Exp. Fluids, 54, 1508, (2013)
[41] Lighthill, M. J.1963Introduction: boundary layer theory. In Laminar Boundary Layer Theory (ed. Rosenhead, L.), pp. 46-113. Oxford University Press.
[42] 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)
[43] Malik, M. R., Numerical methods for hypersonic boundary layer stability, J. Comput. Phys., 86, 376-413, (1990) · Zbl 0682.76043
[44] Moin, P.; Kim, J., The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations, J. Fluid Mech., 155, 441-464, (1985)
[45] Moin, P.; Leonard, A.; Kim, J., Evolution of a curved vortex filament into a vortex ring, Phys. Fluids, 29, 955, (1986)
[46] Morkovin, M. V.1984Bypass transition to turbulence and research desiderta. In Transition in Turbines, , pp. 162-204.
[47] Perry, A. E.; Chong, M. S., On the mechanism of wall turbulence, J. Fluid Mech., 119, 173-217, (1982) · Zbl 0517.76057
[48] Pope, S. B., Turbulent Flows, (2000), Cambridge University Press · Zbl 0966.76002
[49] Pullin, D. I.; Yang, Y., Whither vortex tubes?, Fluid Dyn. Res., 46, (2014)
[50] Rist, U.; Fasel, H., Direct numerical-simulation of controlled transition in a flat-plate boundary-layer, J. Fluid Mech., 298, 211-248, (1995) · Zbl 0850.76392
[51] Robinson, S. K., Coherent motions in the turbulent boundary layer, Annu. Rev. Fluid Mech., 23, 601-639, (1991)
[52] Sandham, N. D.; Kleiser, L., The late stages of transition to turbulence in channel flow, J. Fluid Mech., 245, 319-348, (1992) · Zbl 0825.76312
[53] Sayadi, T.; Hamman, C. W.; Moin, P., Direct numerical simulation of complete H-type and K-type transitions with implications for the dynamics of turbulent boundary layers, J. Fluid Mech., 724, 480-509, (2013) · Zbl 1287.76138
[54] 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
[55] Schlatter, P.; Stolz, S.; Kleiser, L., LES of transitional flow using the approximate deconvolution model, Intl J. Heat Fluid Flow, 25, 3, 549-558, (2004)
[56] Spalart, P. R.; Moser, R. D.; Rogers, M. M., Spectral methods for the Navier-Stokes equations with one infinite and two periodic directions, J. Comput. Phys., 96, 297-324, (1991) · Zbl 0726.76074
[57] Wallace, J. M., Highlights from 50 years of turbulent boundary layer research, J. Turbul., 13, 1-70, (2013)
[58] Wang, B.2015 The investigation on the shock wave/boundary – layer interaction and flow field organization. PhD thesis, National University of Defense Technology, Changsha, China.
[59] Willmarth, W. W.; Lu, S. S., Structure of the Reynolds stress near the wall, J. Fluid Mech., 55, 65-92, (1972)
[60] Wu, J. Z.; Ma, H. Y.; Zhou, M. D., Vorticity and Vortex Dynamics, (2005), Springer
[61] 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
[62] Yan, Y.; Chen, C.; Fu, H.; Liu, C., DNS study on \({\textit\lambda}\)-vortex and vortex ring formation in flow transition at match number 0.5, J. Turbul., 15, 1-21, (2014)
[63] Yang, Y.; Pullin, D. I., On Lagrangian and vortex-surface fields for flows with Taylor-Green and Kida-Pelz initial conditions, J. Fluid Mech., 661, 446-481, (2010) · Zbl 1205.76069
[64] Yang, Y.; Pullin, D. I., Evolution of vortex-surface fields in viscous Taylor-Green and Kida-Pelz flows, J. Fluid Mech., 685, 146-164, (2011) · Zbl 1241.76143
[65] Yang, Y.; Pullin, D. I., Geometric study of Lagrangian and Eulerian structures in turbulent channel flow, J. Fluid Mech., 674, 67-92, (2011) · Zbl 1241.76289
[66] Yang, Y.; Pullin, D. I.; Bermejo-Moreno, I., Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence, J. Fluid Mech., 654, 233-270, (2010) · Zbl 1193.76062
[67] Zhao, Y.; Xia, Z.; Shi, Y.; Xiao, Z.; Chen, S., Constrained large-eddy simulation of laminar – turbulent transition in channel flow, Phys. Fluids, 26, (2014)
[68] 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
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