Skip to main content
×
×
Home

Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions

  • Matteo de Giovanetti (a1), Hyung Jin Sung (a2) and Yongyun Hwang (a1)
Abstract

It has often been proposed that the formation of large-scale motion (or bulges) is a consequence of successive mergers and/or growth of near-wall hairpin vortices. In the present study, we report our direct observation that large-scale motion is generated by an instability of an ‘amplified’ streaky motion in the outer region (i.e. very-large-scale motion). We design a numerical experiment in turbulent channel flow up to $Re_{\unicode[STIX]{x1D70F}}\simeq 2000$ where a streamwise-uniform streaky motion is artificially driven by body forcing in the outer region computed from the previous linear theory (Hwang & Cossu, J. Fluid Mech., vol. 664, 2015, pp. 51–73). As the forcing amplitude is increased, it is found that an energetic streamwise vortical structure emerges at a streamwise wavelength of $\unicode[STIX]{x1D706}_{x}/h\simeq 1{-}5$ ( $h$ is the half-height of the channel). The application of dynamic mode decomposition and the examination of turbulence statistics reveal that this structure is a consequence of the sinuous-mode instability of the streak, a subprocess of the self-sustaining mechanism of the large-scale outer structures. It is also found that the statistical features of the vortical structure are remarkably similar to those of the large-scale motion in the outer region. Finally, it is proposed that the largest streamwise length of the streak instability determines the streamwise length scale of very-large-scale motion.

Copyright
Corresponding author
Email address for correspondence: m.de-giovanetti14@imperial.ac.uk
References
Hide All
Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.
Adrian, R. J., Balachandar, S. & Liu, Z. C. 2001 Spanwise growth of vortex structure in wall turbulence. KSME Intl J. 15 (12), 17411749.
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), 4144.
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. 2006 Self-similar vortex clusters in the turbulent logarithmic region. J. Fluid Mech. 561, 329358.
Alizard, F. 2015 Linear stability of optimal streaks in the log-layer of turbulent channel flows. Phys. Fluids 27 (10), 105103.
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 2960.
Baltzer, J. R., Adrian, R. J. & Wu, X. 2013 Structural organization of large and very-large scales in turbulent pipe flow simulation. J. Fluid Mech. 720, 236279.
Blackwelder, R. F. & Eckelmann, H. 1979 Streamwise vortices associated with the bursting phenomenon. J. Fluid Mech. 94, 577594.
Butler, K. M. & Farrell, B. F. 1993 Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids 3 (5), 774777.
Canton, J., Örlü, R., Chin, C. & Schlatter, P. 2016 Reynolds number dependence of large-scale friction control in turbulent channel flow. Phys. Rev. Fluids 1 (8), 081501.
Cassinelli, A., de Giovanetti, M. & Hwang, Y. 2017 Streak instability in near-wall turbulence revisited. J. Turbul. 18 (5), 443464.
Chernyshenko, S. I. & Baig, M. F. 2005 The mechanism of streak formation in near-wall turbulence. J. Fluid Mech. 544, 99131.
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. 2006 Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech. 566, 357376.
Flores, O. & Jiménez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22 (7), 14.
de Giovanetti, M., Hwang, Y. & Choi, H. 2016 Skin-friction generation by attached eddies in turbulent channel flow. J. Fluid Mech. 808, 511538.
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.
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 112.
Hoepffner, J., Brandt, L. & Henningson, D. S. 2005 Transient growth on boundary layer streaks. J. Fluid Mech. 537, 91100.
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to Re 𝜏 = 2003. Phys. Fluids 18, 14.
Hutchins, N. & Marusic, I. 2007 Large-scale influences in near-wall turbulence. Phil. Trans. R. Soc. Lond. A 365 (1852), 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 flows. Phys. Rev. Fluids 1, 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 Amplification of coherent streaks in the turbulent Couette flow: an input–output analysis at low Reynolds number. J. Fluid Mech. 643, 333348.
Hwang, Y. & Cossu, C. 2010b Linear non-normal energy amplification of harmonic and stochastic forcing in the turbulent channel flow. J. Fluid Mech. 664, 5173.
Hwang, Y. & Cossu, C. 2010c Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 110.
Hwang, Y. & Cossu, C. 2011 Self-sustained processes in the logarithmic layer of turbulent channel flows. Phys. Fluids 23 (6), 061702.
Hwang, Y., Willis, A. P. & Cossu, C. 2016 Invariant solutions of minimal large-scale structures in turbulent channel flow for Re up to 1000. J. Fluid Mech. 802, R1.
Jeong, J. & Hussain, F. 1997 Coherent structures near the wall in a turbulent channel flow. J. Fluid Mech. 332, 185214.
Jiménez, J. 2013a How linear is wall-bounded turbulence? Phys. Fluids 25 (11), 110814.
Jiménez, J. 2013b Near-wall turbulence. Phys. Fluids 25 (10), 101302.
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.
Jovanović, M. R., Schmid, P. J. & Nichols, J. W. 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26 (2), 122.
Kim, H. T., Kline, S. J. & Reynolds, W. C. 1971 The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50 (1), 133160.
Kim, J. 2011 Physics and control of wall turbulence for drag reduction. Phil. Trans. R. Soc. Lond. A 369 (1940), 13961411.
Kim, J., Moin, P. & Moser, R. D. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11 (2), 417422.
Kline, S. J., Reynolds, W. C., Schraub, F. A. & Rundstatler, P. W. 1967 The structure of turbulent boundary layers. J. Fluid Mech. 30, 741773.
Kovasznay, L. S. G. 1970 The turbulent boundary layer. Annu. Rev. Fluid Mech. 2, 95112.
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Comput. Phys. 98, 243251.
Marusic, I., Monty, J. P., Hultmark, M. & Smits, A. J. 2013 On the logarithmic region in wall turbulence. J. Fluid Mech. 716, R3 111.
Monty, J. P., Hutchins, N., Ng, H. C. H., Marusic, I. & Chong, M. S. 2009 A comparison of turbulent pipe, channel and boundary layer flows. J. Fluid Mech. 632, 431442.
Nickels, T. B., Marusic, I., Hafez, S. & Chong, M. S. 2005 Evidence of the k 1 -1 law in a high-Reynolds-number turbulent boundary layer. Phys. Rev. Lett. 95 (7), 14.
Park, D. S. & Huerre, P. 1995 Primary and secondary instabilities of the asymptotic suction boundary layer on a curved plate. J. Fluid Mech. 283, 249272.
Park, J., Hwang, Y. & Cossu, C. 2011 On the stability of large-scale streaks in turbulent Couette and Poiseulle flows. C. R. Méc. 339 (1), 15.
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 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, 389407.
Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21 (1), 16.
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263288.
Reynolds, W. C. & Tiederman, W. G. 1967 Stability of turbulent channel flow, with application to Malkus’s theory. J. Fluid Mech. 27 (2), 253272.
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 528.
Schmid, P. J. & Henningson, D. S. 2001 Stability and Transition in Shear Flows. Springer.
Schoppa, W. & Hussain, F. 1998 Genesis of longitudinal vortices in near-wall turbulence. Meccanica 33 (5), 489501.
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.
Sharma, A. S. & McKeon, B. J. 2013 On coherent structure in wall turbulence. J. Fluid Mech. 728, 196238.
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, 2754.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Townsend, A. A. 1961 Equilibrium layers and wall turbulence. J. Fluid Mech. 12, 97120.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 1st edn. Cambridge University Press.
Vreman, A. W. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 36703681.
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9 (4), 883900.
Willis, A. P., Hwang, Y. & Cossu, C. 2010 Optimally amplified large-scale streaks and drag reduction in turbulent pipe flow. Phys. Rev. E 82 (3), 111.
Zare, A., Jovanović, M. R. & Georgiou, T. 2017 Colour of turbulence. J. Fluid Mech. 812, 636680.
Zhou, J., Adrian, R. J., Balachandar, S. & Kendall, T. M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification