Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T16:33:11.809Z Has data issue: false hasContentIssue false
  • English
  • Français

Identity of attached eddies in turbulent channel flows with bidimensional empirical mode decomposition

Published online by Cambridge University Press:  15 May 2019

Cheng Cheng ,
Weipeng Li Open the ORCID record for Weipeng Li [Opens in a new window] ,
Adrián Lozano-Durán Open the ORCID record for Adrián Lozano-Durán [Opens in a new window]  and
Hong Liu
Cheng Cheng
Affiliation:
School of Aeronautics and Astronautics, Shanghai JiaoTong University, Shanghai 200240, PR China
Weipeng Li*
Affiliation:
School of Aeronautics and Astronautics, Shanghai JiaoTong University, Shanghai 200240, PR China
Adrián Lozano-Durán
Affiliation:
Center for Turbulence Research, Stanford University, CA 94305, USA
Hong Liu
Affiliation:
School of Aeronautics and Astronautics, Shanghai JiaoTong University, Shanghai 200240, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Bidimensional empirical mode decomposition (BEMD) is used to identify attached eddies in turbulent channel flows and quantify their relationship with the mean skin-friction drag generation. BEMD is an adaptive, non-intrusive, data-driven method for mode decomposition of multiscale signals especially suitable for non-stationary and nonlinear processes such as those encountered in turbulent flows. In the present study, we decompose the velocity fluctuations obtained by direct numerical simulation of channel flows into BEMD modes characterized by specific length scales. Unlike previous works (e.g. Flores & Jiménez, Phys. Fluids, vol. 22(7), 2010, 071704; Hwang, J. Fluid Mech., vol. 767, 2015, pp. 254–289), the current approach employs naturally evolving wall-bounded turbulence without modifications of the Navier–Stokes equations to maintain the inherent turbulent dynamics, and minimize artificial numerical enforcement or truncation. We show that modes identified by BEMD exhibit a self-similar behaviour, and that single attached eddies are mainly composed of streaky structures carrying intense streamwise velocity fluctuations and vortex packets permeating in all velocity components. Our findings are consistent with the existence of attached eddies in actual wall-bounded flows, and show that BEMD modes are tenable candidates to represent Townsend attached eddies. Finally, we evaluate the turbulent-drag generation from the perspective of attached eddies with the aid of the Fukagata–Iwamoto–Kasagi identity (Fukagata et al., Phys. Fluids, vol. 14(11), 2002, pp. L73–L76) by splitting the Reynolds shear stress into four different terms related to the length scale of the attached eddies.

JFM classification

Boundary Layers: Boundary layer structure Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 1037 - 1071
Copyright
© 2019 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbassi, M. R., Baars, W. J., Hutchins, N. & Marusic, I. 2017 Skin-friction drag reduction in a high-Reynolds-number turbulent boundary layer via real-time control of large-scale structures. Intl J. Heat Fluid Flow 67, 30–41.Google Scholar
Agostini, L. & Leschziner, M. 2014 On the influence of outer large-scale structures on near-wall turbulence in channel flow. Phys. Fluids 26 (7), 075107.Google Scholar
Agostini, L. & Leschziner, M. 2016 Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28 (1), 339–352.Google Scholar
Agostini, L. & Leschziner, M. 2017 Spectral analysis of near-wall turbulence in channel flow at Re 𝜏 = 4200 with emphasis on the attached-eddy hypothesis. Phys. Rev. Fluids 2, 014603.Google Scholar
Agostini, L. & Leschziner, M. 2018 The impact of footprints of large-scale outer structures on the near-wall layer in the presence of drag-reducing spanwise wall motion. Flow Turbul. Combust. 100, 1–25.Google Scholar
Agostini, L., Leschziner, M., Poggie, J., Bisek, N. J. & Gaitonde, D. 2017 Multi-scale interactions in a compressible boundary layer. J. Turbul. 18, 1–21.Google Scholar
Andelman, D., Cates, M. E., Roux, D. & Safran, S. A. 1987 Structure and phase equilibria of microemulsions. J. Chem. Phys. 87 (12), 7229–7241.Google Scholar
Ansell, P. J. & Balajewicz, M. J. 2016 Separation of unsteady scales in a mixing layer using empirical mode decomposition. AIAA J. 55 (2), 419–434.Google Scholar
Bookstein, F. L. 1989 Principal warps: thin-plate splines and the decomposition of deformations. IEEE Trans. Pattern Anal. Mach. Intell. 11 (6), 567–585.Google Scholar
Carr, J. C., Fright, W. R. & Beatson, R. K. 1997 Surface interpolation with radial basis functions for medical imaging. IEEE Trans. Med. Imaging 16 (1), 96–107.Google Scholar
Chang, Y., Collis, S. S. & Ramakrishnan, S. 2002 Viscous effects in control of near-wall turbulence. Phys. Fluids 14 (11), 4069–4080.Google Scholar
Cho, M., Hwang, Y. & Choi, H. 2018 Scale interactions and spectral energy transfer in turbulent channel flow. J. Fluid Mech. 854, 474–504.Google Scholar
Choi, H., Moin, P. & Kim, J. 1993 Direct numerical simulation of turbulent flow over riblets. J. Fluid Mech. 255, 503–539.Google Scholar
Choi, H., Moin, P. & Kim, J. 1994 Active turbulence control for drag reduction in wall-bounded flows. J. Fluid Mech. 262, 75–110.Google Scholar
De Silva, C. M., Kevin, K., Baidya, R., Hutchins, N. & Marusic, I. 2018 Large coherence of spanwise velocity in turbulent boundary layers. J. Fluid Mech. 847, 161–185.Google Scholar
De Silva, C. M., Marusic, I. & Hutchins, N. 2016 Uniform momentum zones in turbulent boundary layers. J. Fluid Mech. 786, 309–331.Google Scholar
Dean, R. B. 1978 Reynolds number dependence of skin friction and other bulk flow variables in two-dimensional rectangular duct flow. J. Fluids Engng 100 (2), 215–223.Google Scholar
Deck, S., Renard, N., Laraufie, R. & Weiss, P. 2014 Large-scale contribution to mean wall shear stress in high-Reynolds-number flat-plate boundary layers up to Re 𝜃 = 13 650. J. Fluid Mech. 743, 202–248.Google Scholar
Del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144.Google Scholar
Del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329–358.Google Scholar
Dong, S., Lozano-Durán, A., Sekimoto, A. & Jiménez, J. 2017 Coherent structures in statistically stationary homogeneous shear turbulence. J. Fluid Mech. 816, 167–208.Google Scholar
Encinar, M. P., Lozano-Durán, A. & Jiménez, J. 2018 Reconstructing channel turbulence from wall observations. In Procs. CTR Summer School, Stanford University, (in press).Google Scholar
Feldmann, D. & Avila, M. 2018 Overdamped large-eddy simulations of turbulent pipe flow up to Re 𝜏 = 1500. J. Phys.: Conf. Ser. 1001, 012016.Google Scholar
Feng, Z., Zhang, D. & Zuo, M. J. 2017 Adaptive mode decomposition methods and their applications in signal analysis for machinery fault diagnosis: a review with examples. IEEE Access 5, 24301–24331.Google Scholar
Flores, O. & Jiménez, J. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566 (566), 357–376.Google Scholar
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 071704.Google Scholar
Flores, O., Jiménez, J. & Del Álamo, J. C. 2007 Vorticity organization in the outer layer of turbulent channels with disturbed walls. J. Fluid Mech. 591 (591), 145–154.Google Scholar
Fukagata, K., Iwamoto, K. & Kasagi, N. 2002 Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids 14 (11), L73–L76.Google Scholar
Gatti, D., Quadrio, M. & Frohnapfel, B. 2015 Reynolds number effect on turbulent drag reduction. In 15th European Turbulence Conference (ETC15). University of Delft.Google Scholar
de Giovanetti, M., Hwang, Y. & Choi, H. 2016 Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech. 808, 511–538.Google Scholar
de Giovanetti, M., Sung, H. J. & Hwang, Y. 2017 Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions. J. Fluid Mech. 832, 483–513.Google Scholar
Gad-el Hak, M. 1994 Interactive control of turbulent boundary layers – a futuristic overview. AIAA J. 32 (9), 1753–1765.Google Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.Google Scholar
Hellström, L. H. O., Marusic, I. & Smits, A. J. 2016 Self-similarity of the large-scale motions in turbulent pipe flow. J. Fluid Mech. 792, R1.Google Scholar
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.Google Scholar
Huang, Y. X., Schmitt, F., Lu, Z. M. & Liu, Y. L. 2008 An amplitude–frequency study of turbulent scaling intermittency using empirical mode decomposition and Hilbert spectral analysis. Europhys. Lett. 84 (4), 40010.Google Scholar
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N. C., Tung, C. C. & Liu, H. H. 1998 The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. A 454, 903–995.Google Scholar
Hutchins, N. & Marusic, I. 2007 Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech. 579, 1–28.Google Scholar
Hwang, Y. 2013 Near-wall turbulent fluctuations in the absence of wide outer motions. J. Fluid Mech. 723 (5), 264–288.Google Scholar
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254–289.Google Scholar
Hwang, Y. 2016 Mesolayer of attached eddies in turbulent channel flow. Phys. Rev. Fluids 1 (6), 064401.Google Scholar
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708–738.Google Scholar
Hwang, Y. & Cossu, C. 2010 Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 044505.Google Scholar
Hwang, Y. & Cossu, C. 2011 Self-sustained processes in the logarithmic layer of turbulent channel flows. Phys. Fluids 23 (6), 061702.Google Scholar
Hwang, J. & Sung, H. J. 2018 Wall-attached structures of velocity fluctuations in a turbulent boundary layer. J. Fluid Mech. 856, 958–983.Google Scholar
Jeong, J., Hussain, F., Schoppa, W. & Kim, J. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185–214.Google Scholar
Jiang, G. & Shu, C. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202–228.Google Scholar
Jiménez, J. 2012 Cascades in wall-bounded turbulence. Annu. Rev. Fluid Mech. 44 (1), 27–45.Google Scholar
Jiménez, J. 2013 Near-wall turbulence. Phys. Fluids 25 (10), 97–120.Google Scholar
Jiménez, J. 2018 Coherent structures in wall-bounded turbulence. J. Fluid Mech. 842, P1.Google Scholar
Jiménez, J., Del Álamo, J. C. & Flores, O. 2004 The large-scale dynamics of near-wall turbulence. J. Fluid Mech. 505, 179–199.Google Scholar
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215–236.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.Google Scholar
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.Google Scholar
Jin, L., Ahn, J. & Sung, H.J. 2015 Comparison of large- and very-large-scale motions in turbulent pipe and channel flows. Phys. Fluids 27 (2), 431–442.Google Scholar
Jung, W. J., Mangiavacchi, N. & Akhavan, R. 1992 Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations. Phys. Fluids A 4 (8), 1605–1607.Google Scholar
Karniadakis, G. E. & Choi, K. 2003 Mechanisms on transverse motions in turbulent wall flows. Annu. Rev. Fluid Mech. 35 (35), 45–62.Google Scholar
Kawai, S. 2016 Direct numerical simulation of transcritical turbulent boundary layers at supercritical pressures with strong real fluid effects. In 54th AIAA Aerospace Sciences Meeting, p. 1934.Google Scholar
Kim, K. C. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417–422.Google Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177 (177), 133–166.Google Scholar
Lee, J., Lee, J., Choi, J. & Sung, H. 2014 Spatial organization of large- and very-large-scale motions in a turbulent channel flow. J. Fluid Mech. 749, 818–840.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395–415.Google Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1), 16–42.Google Scholar
Lenormand, E., Sagaut, P. & Ta Phuoc, L. 2000 Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number. Intl J. Numer. Meth. Fluids 32 (4), 369–406.Google Scholar
Li, W., Nonomura, T. & Fujii, K. 2013a Mechanism of controlling supersonic cavity oscillations using upstream mass injection. Phys. Fluids 25 (8), 086101.Google Scholar
Li, W., Nonomura, T. & Fujii, K. 2013b On the feedback mechanism in supersonic cavity flows. Phys. Fluids 25 (5), 056101.Google Scholar
Li, W. & Wang, L. 2018 Geometrical structure analysis of a zero-pressure-gradient turbulent boundary layer. J. Fluid Mech. 846, 318–340.Google Scholar
Lozano-Durán, A. & Borrell, G. 2016 Algorithm 964: an efficient algorithm to compute the genus of discrete surfaces and applications to turbulent flows. ACM Trans. Math. Softw. 42 (4), 34:1–34:19.Google Scholar
Lozano-Durán, A., Flores, O. & Jiménez, J. 2012 The three-dimensional structure of momentum transfer in turbulent channels. J. Fluid Mech. 694, 100–130.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014a Effect of the computational domain on direct simulations of turbulent channels up to Re 𝜏 = 4200. Phys. Fluids 26 (1), 011702.Google Scholar
Lozano-Durán, A. & Jiménez, J. 2014b Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432–471.Google Scholar
Marusic, I. & Kunkel, G. J. 2003 Streamwise turbulence intensity formulation for flat-plate boundary layers. Phys. Fluids 15 (8), 2461–2464.Google Scholar
Marusic, I., McKeon, B. J., Monkewitz, P. A., Nagib, H. M., Smits, A. J. & Sreenivasan, K. R. 2010 Wall-bounded turbulent flows at high Reynolds numbers: recent advances and key issues. Phys. Fluids 22 (6), 065103.Google Scholar
Marusic, I. & Monty, J. P. 2019 Attached eddy model of wall turbulence. Annu. Rev. Fluid Mech. 51, 49–74.Google Scholar
Marusic, I. & Woodcock, J. D. 2014 Attached eddies and high-order statistics. In Progress in Wall Turbulence: Understanding and Modelling, pp. 47–60. Springer.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boundary layers. J. Fluid Mech. 628, 311–337.Google Scholar
Mathis, R., Hutchins, N. & Marusic, I. 2011 A predictive inner–outer model for streamwise turbulence statistics in wall-bounded flows. J. Fluid Mech. 681, 537–566.Google Scholar
Metzger, M. M. & Klewicki, J. C. 2001 A comparative study of near-wall turbulence in high and low Reynolds number boundary layers. Phys. Fluids 13 (3), 692–701.Google Scholar
Nunes, J. C., Bouaoune, Y., Delechelle, E., Niang, O. & Bunel, P. 2003 Image analysis by bidimensional empirical mode decomposition. Image Vis. Comput. 21 (12), 1019–1026.Google Scholar
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119 (119), 173–217.Google Scholar
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163–199.Google Scholar
Perry, A. E. & Marusic, I. 1995 A wall-wake model for the turbulence structure of boundary layers. Part 1. Extension of the attached eddy hypothesis. J. Fluid Mech. 298 (298), 361–388.Google Scholar
Pirozzoli, S. & Bernardini, M. 2013 Probing high-Reynolds-number effects in numerical boundary layers. Phys. Fluids 25 (2), 319–346.Google Scholar
Robinson, S. K.1991 The kinematics of turbulent boundary layer structure. NASA STI/Recon Technical Report No. 91.Google Scholar
Samie, M., Marusic, I., Hutchins, N., Fu, M. K., Fan, Y., Hultmark, M. & Smits, A. J. 2018 Fully resolved measurements of turbulent boundary layer flows up to Re 𝜏 = 20 000. J. Fluid Mech. 851, 391–415.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.Google Scholar
Smith, C. R. & Metzler, S. P. 1983 The characteristics of low-speed streaks in the near-wall region of a turbulent boundary layer. J. Fluid Mech. 129, 27–54.Google Scholar
Smits, A. J., McKeon, B. J. & Marusic, I. 2011 High-Reynolds number wall turbulence. Annu. Rev. Fluid Mech. 43, 353–375.Google Scholar
Tardu, S. 2011 Statistical Approach to Wall Turbulence. ISTE, John Wiley.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2002 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490 (490), 37–74.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2005 Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer. J. Fluid Mech. 545, 141–162.Google Scholar
Touber, E. & Leschziner, M. A. 2012 Near-wall streak modification by spanwise oscillatory wall motion and drag-reduction mechanisms. J. Fluid Mech. 693, 150–200.Google Scholar
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 11 (1), 97–120.Google Scholar
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.Google Scholar
Woodcock, J. D. & Marusic, I. 2015 The statistical behaviour of attached eddies. Phys. Fluids 27 (1), 97–120.Google Scholar