Skip to main content Accessibility help

Scale interactions and spectral energy transfer in turbulent channel flow

  • Minjeong Cho (a1), Yongyun Hwang (a2) and Haecheon Choi (a1) (a3)


Spectral energy transfer in a turbulent channel flow is investigated at Reynolds number $Re_{\unicode[STIX]{x1D70F}}\simeq 1700$ , based on the wall shear velocity and channel half-height, with a particular emphasis on full visualization of triadic wave interactions involved in turbulent transport. As in previous studies, turbulent production is found to be almost uniform, especially over the logarithmic region, and the related spanwise integral length scale is approximately proportional to the distance from the wall. In the logarithmic and outer regions, the energy balance at the integral length scales is mainly formed between production and nonlinear turbulent transport, the latter of which plays the central role in the energy cascade down to the Kolmogorov microscale. While confirming the classical role of the turbulent transport, the triadic wave interaction analysis unveils two new types of scale interaction processes, highly active in the near-wall and the lower logarithmic regions. First, for relatively small energy-containing motions, part of the energy transfer mechanisms from the integral to the adjacent small length scale in the energy cascade is found to be provided by the interactions between larger energy-containing motions. It is subsequently shown that this is related to involvement of large energy-containing motions in skin-friction generation. Second, there exists a non-negligible amount of energy transfer from small to large integral scales in the process of downward energy transfer to the near-wall region. This type of scale interaction is predominant only for the streamwise and spanwise velocity components, and it plays a central role in the formation of the wall-reaching inactive part of large energy-containing motions. A further analysis reveals that this type of scale interaction leads the wall-reaching inactive part to scale in the inner units, consistent with the recent observation. Finally, it is proposed that turbulence production and pressure–strain spectra support the existence of the self-sustaining process as the main turnover dynamics of all the energy-containing motions.


Corresponding author

Email address for correspondence:


Hide All
Agostini, L. & Leschziner, M. 2016 Predicting the response of small-scale near-wall turbulence to large-scale outer motions. Phys. Fluids 28 (1), 015107.
Agostini, L., Leschziner, M. & Gaitonde, D. 2016 Skewness-induced asymmetric modulation of small-scale turbulence by large-scale structures. Phys. Fluids 28 (1), 015110.
Agostini, L., Leschziner, M. & Gaitonde, D. 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.
Agostini, L., Touber, E. & Leschziner, M. A. 2014 Spanwise oscillatory wall motion in channel flow: drag-reduction mechanisms inferred from DNS-predicted phase-wise property variations at Re 𝜏 = 1000. J. Fluid Mech. 743, 606635.
del Álamo, J. C. & Jiménez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205213.
del Álamo, J. C. & Jiménez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
del Álamo, J. C., Jiménez, J., Zandonade, P. & Moser, R. D. 2004 Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135144.
Baars, W. J., Hutchins, N. & Marusic, I. 2017 Self-similarity of wall-attached turbulence in boundary layers. J. Fluid Mech. 823, R2.
Bradshaw, P. 1967 ‘Inactive’ motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30 (2), 241258.
Butler, K. M. & Farrell, B. F. 1993 Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids 5, 774777.
Cassinelli, A., de Giovanetti, M. & Hwang, Y. 2017 Streak instability in near-wall turbulence revisited. J. Turbul. 18 (5), 443464.
Cho, M., Choi, H. & Hwang, Y. 2016 On the structure of pressure fluctuations of self-sustaining attached eddies. Bull. Am. Phys. Soc. 61 (20), A33.003.
Chung, D., Monty, J. P. & Ooi, A. 2014 An idealised assessment of townsend’s outer-layer similarity hypothesis for wall turbulence. J. Fluid Mech. 742, R3.
Cossu, C., Pujals, G. & Depardon, S. 2009 Optimal transient growth and very large scale structures in turbulent boundary layers. J. Fluid Mech. 619, 7994.
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, 145154.
Gayme, D. F., Mckeon, B. J., Papachristodoulou, A., Bamieh, B. & Doyle, J. C. 2010 A streamwise constant model of turbulence in plane Couette flow. J. Fluid Mech. 665, 99119.
de Giovanetti, M., Hwang, Y. & Choi, H. 2016 Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech. 808, 511538.
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, 483513.
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
Henningson, D. S. 1996 Comment on ‘transition in shear flows, nonlinear normality versus non-normal linearity’ [Phys. Fluids 7, 3060 (1995)]. Phys. Fluids 8, 22572258.
Ho, C. M. & Huerre, P. 1984 Perturbed shear layers. Annu. Rev. Fluid Mech. 16, 365424.
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20, 101511.
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365, 647664.
Hwang, Y. 2013 Near-wall turbulent fluctuations in the absence of wide outer motions. J. Fluid Mech. 723, 264288.
Hwang, Y. 2015 Statistical structure of self-sustaining attached eddies in turbulent channel flow. J. Fluid Mech. 767, 254289.
Hwang, Y. 2016 Mesolayer of attached eddies in turbulent channel flow. Phys. Rev. Fluids 1 (6), 064401.
Hwang, Y. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708738.
Hwang, Y. & Cossu, C. 2010a Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664, 5173.
Hwang, Y. & Cossu, C. 2010b Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105, 044505.
Hwang, Y. & Cossu, C. 2011 Self-sustained processes in the logarithmic layer of turbulent channel flows. Phys. Fluids 23, 061702.
Jiménez, J. & Hoyas, S. 2008 Turbulent fluctuations above the buffer layer of wall-bounded flows. J. Fluid Mech. 611, 215236.
Jiménez, J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.
Jiménez, J. & Wray, A. A. 1998 On the characteristics of vortex filaments in isotropic turbulence. J. Fluid Mech. 373, 255285.
Joseph, D. D. 1976 Stability of Fluid Motions. Springer.
Kawata, T. & Alfredsson, P. H. 2018 Inverse interscale transport of the reynolds shear stress in plane couette turbulence. Phys. Rev. Lett. 120, 244501.
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 209303.
Kolmogorov, A. N. 1991 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proc. R. Soc. Lond. A 434, 913.
Kovasznay, L. S. G., Kibens, V. & Blackwelder, R. F. 1970 Large-scale motion in the intermittent region of a turbulent boundary layer. J. Fluid Mech. 41, 283325.
Lee, J., Choi, H. & Park, N. 2010 Dynamic global model for large eddy simulation of transient flow. Phys. Fluids 22, 075106.
Lee, M. & Moser, R. D. 2015a Spectral analysis on Reynolds stress transport equation in high Re wall-bounded turbulence. In 9th Iternational Symposium on Turbulence and Shear Flow Phenomena, Melbourne, Australia, pp. 4A-3.
Lee, M. & Moser, R. D. 2015b Direct numerical simulation of turbulent channel flow up to Re 𝜏 ≈ 5200. J. Fluid Mech. 774, 395415.
Lozano-Durán, A. & Jiménez, J. 2014 Time-resolved evolution of coherent structures in turbulent channels: characterization of eddies and cascades. J. Fluid Mech. 759, 432471.
Malkus, W. V. R. 1956 Outline of a theory of turbulent shear flow. J. Fluid Mech. 1, 521539.
Marusic, I. 2001 On the role of large-scale structures in wall turbulence. Phys. Fluids 13, 735743.
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3.
Mathis, R., Hutchins, N. & Marusic, I. 2009 Large-scale amplitude modulation of the small-scale structures in turbulent boudnary layers. J. Fluid. Mech. 628, 311337.
Mizuno, Y. 2016 Spectra of energy transport in turbulent channel flows for moderate Reynolds numbers. J. Fluid Mech. 805, 171187.
Park, N., Lee, S., Lee, J. & Choi, H. 2006 A dynamic subgrid-scale eddy viscosity model with a global model coefficient. Phys. Fluids 18, 125109.
Perry, A. E. & Chong, M. S. 1982 On the mechanism of wall turbulence. J. Fluid Mech. 119, 173217.
Perry, A. E., Henbest, S. & Chong, M. S. 1986 A theoretical and experimental study of wall turbulence. J. Fluid Mech. 165, 163199.
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, 361388.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21, 015109.
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.
Talluru, K. M., Baidya, R., Hutchins, N. & Marusic, I. 2014 Amplitude modulation of all three velocity components in turbulent boundary layers. J. Fluid Mech. 746, R1.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow. Cambridge University Press.
Vassilicos, J. C. 2015 Dissipation in turbulent flows. Annu. Rev. Fluid Mech. 47, 95114.
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883900.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

Scale interactions and spectral energy transfer in turbulent channel flow

  • Minjeong Cho (a1), Yongyun Hwang (a2) and Haecheon Choi (a1) (a3)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.