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Optimal bursts in turbulent channel flow

Published online by Cambridge University Press:  15 March 2017

Mirko Farano Open the ORCID record for Mirko Farano [Opens in a new window] ,
Stefania Cherubini Open the ORCID record for Stefania Cherubini [Opens in a new window] ,
Jean-Christophe Robinet  and
Pietro De Palma
Mirko Farano*
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy DynFluid Laboratory, Arts et Métiers ParisTech, 151 Boulevard de l’Hôpital, 75013 Paris, France
Stefania Cherubini
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy DynFluid Laboratory, Arts et Métiers ParisTech, 151 Boulevard de l’Hôpital, 75013 Paris, France
Jean-Christophe Robinet
Affiliation:
DynFluid Laboratory, Arts et Métiers ParisTech, 151 Boulevard de l’Hôpital, 75013 Paris, France
Pietro De Palma
Affiliation:
DMMM, Politecnico di Bari, Via Re David 200, 70125 Bari, Italy
*
†Email address for correspondence: [email protected]
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Abstract

Bursts are recurrent, transient, highly energetic events characterized by localized variations of velocity and vorticity in turbulent wall-bounded flows. In this work, a nonlinear energy optimization strategy is employed to investigate whether the origin of such bursting events in a turbulent channel flow can be related to the presence of high-amplitude coherent structures. The results show that bursting events correspond to optimal energy flow structures embedded in the fully turbulent flow. In particular, optimal structures inducing energy peaks at short time are initially composed of highly oscillating vortices and streaks near the wall. At moderate friction Reynolds numbers, through the bursts, energy is exchanged between the streaks and packets of hairpin vortices of different sizes reaching the outer scale. Such an optimal flow configuration reproduces well the spatial spectra as well as the probability density function typical of turbulent flows, recovering the mechanism of direct-inverse energy cascade. These results represent an important step towards understanding the dynamics of turbulence at moderate Reynolds numbers and pave the way to new nonlinear techniques to manipulate and control the self-sustained turbulence dynamics.

JFM classification

Boundary Layers: Boundary layer structure Instability: Nonlinear instability Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 817 , 25 April 2017 , pp. 35 - 60
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Copyright
© 2017 Cambridge University Press 

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References

Adrian, R. J. 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.CrossRefGoogle Scholar
Adrian, R. J., Balachandar, S. & Lin, Z. C. 2001 Spanwise growth of vortex structure in wall turbulence. KSME Intl J. 15 (12), 1741–1749.CrossRefGoogle Scholar
del Álamo, J. C. & Jiménez, J. 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41.CrossRefGoogle Scholar
Andersson, P., Brandt, L., Bottaro, A. & Henningson, D. S. 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 29–60.Google Scholar
Barkley, D., Song, B., Mukund, V., Lemoult, G., Avila, M. & Hof, B. 2015 The rise of fully turbulent flow. Nature 526, 550–553.Google Scholar
Blackburn, H. M., Mansour, N. N. & Cantwell, B. J. 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269–292.Google Scholar
Bogard, D. G. & Tiederman, W. G. 1986 Burst detection with single-point velocity measurements. J. Fluid Mech. 162, 389–413.CrossRefGoogle Scholar
Butler, K. M. & Farrell, B. F. 1993 Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids A 5 (3), 774–777.CrossRefGoogle Scholar
Chen, J., Hussain, F., Pei, J. & She, Z.-S. 2014 Velocity–vorticity correlation structure in turbulent channel flow. J. Fluid Mech. 742, 291–307.Google Scholar
Cherubini, S. & De Palma, P. 2013 Nonlinear optimal perturbations in a Couette flow: bursting and transition. J. Fluid Mech. 716, 251–279.Google Scholar
Cherubini, S., De Palma, P. & Robinet, J.-C. 2015 Nonlinear optimals in the asymptotic suction boundary layer: transition thresholds and symmetry breaking. Phys. Fluids 27 (3), 034108.Google Scholar
Cherubini, S., De Palma, P., Robinet, J.-C. & Bottaro, A. 2010 Rapid path to transition via nonlinear localized optimal perturbations in a boundary-layer flow. Phys. Rev. E 82 (6), 066302.Google Scholar
Chong, M. S., Perry, A. E. & Cantwell, B. J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765–777.CrossRefGoogle Scholar
Cossu, C., Pujals, G. & Depardon, S. 2009 Optimal transient growth and very large-scale structures in turbulent boundary layers. J. Fluid Mech. 619, 79–94.CrossRefGoogle Scholar
Deville, M. O., Fischer, P. F. & Mund, E. H. 2002 High-Order Methods for Incompressible Fluid Flow, vol. 9. Cambridge University Press.Google Scholar
Duguet, Y., Monokrousos, A., Brandt, L. & Henningson, D. S. 2013 Minimal transition thresholds in plane Couette flow. Phys. Fluids 25 (8), 084103.Google Scholar
Eitel-Amor, G., Örlü, R., Schlatter, P. & Flores, O. 2015 Hairpin vortices in turbulent boundary layers. Phys. Fluids 27 (2), 025108.CrossRefGoogle Scholar
Faisst, H. & Eckhardt, B. 2003 Travelling waves in pipe flow. Phys. Rev. Lett. 91, 224502.Google Scholar
Farano, M., Cherubini, S., Robinet, J.-C. & De Palma, P. 2015 Hairpin-like optimal perturbations in plane poiseuille flow. J. Fluid Mech. 775, R2.Google Scholar
Farano, M., Cherubini, S., Robinet, J.-C. & De Palma, P. 2016 Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane poiseuille flow. Fluid Dyn. Res. 48, 061409.CrossRefGoogle Scholar
Fischer, P. F., Lottes, J. W. & Kerkemeir, S. G.2008 Nek5000 Web pages. http://nek5000.mcs.anl.gov.Google Scholar
Flores, O. & Jimenez, J. 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22, 071704.Google Scholar
Foures, D. P. G., Caulfield, C. P. & Schmid, P. J. 2013 Localization of flow structures using ∞-norm optimization. J. Fluid Mech. 729, 672–701.CrossRefGoogle Scholar
Hamilton, J. M., Kim, J. & Waleffe, F. 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317–348.CrossRefGoogle Scholar
Heist, D. K., Hanratty, T. J. & Na, Y. 2000 Observations of the formation of streamwise vortices by rotation of arch vortices. Phys. Fluids 12 (11), 2965–2975.CrossRefGoogle Scholar
Hof, B., van Doorne, C. W. H., Westerweel, J., Nieuwstadt, F. T. M., Faisst, H., Eckhardt, B., Wedin, H., Kerswell, R. R. & Waleffe, F. 2004 Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305, 1594–1598.CrossRefGoogle ScholarPubMed
Hoyas, S. & Jiménez, J. 2006 Scaling of the velocity fluctuations in turbulent channels up to re 𝜏 = 2003. Phys. Fluids 18 (1), 011702.CrossRefGoogle Scholar
Hwang, J., Lee, J., Sung, H. J. & Zaki, T. A. 2016 Inner–outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128–157.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. & Bengana, Y. 2016 Self-sustaining process of minimal attached eddies in turbulent channel flow. J. Fluid Mech. 795, 708–738.CrossRefGoogle Scholar
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, 333–348.CrossRefGoogle Scholar
Hwang, Y. & Cossu, C. 2010b Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 044505.CrossRefGoogle ScholarPubMed
Jiménez, J. 1999 The physics of wall turbulence. Physica A 263 (1), 252–262.Google Scholar
Jiménez, J. 2013 How linear is wall-bounded turbulence? Phys. Fluids 25, 110814.CrossRefGoogle Scholar
Jiménez, J. 2015 Direct detection of linearized bursts in turbulence. Phys. Fluids 27, 065102.Google Scholar
Jiménez, J. & Moin, P. 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213–240.CrossRefGoogle Scholar
Jiménez, J. J., Kawahara, G., Simens, M. P., Nagata, N. & Shiba, M. 2005 Characterization of near-wall turbulence in terms of equilibrium and bursting solutions. Phys. Fluids 17, 015105.CrossRefGoogle Scholar
Jiménez, J. J. & Pinelli, A. 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335–359.CrossRefGoogle Scholar
Kim, J., Moin, P. & Moser, R. 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133–166.CrossRefGoogle Scholar
Kline, S. J., Reynold, W. C., Schraub, F. & Rundstander, P. W. 1967 The structure of turbulent boundary layer flows. J. Fluid Mech. 30, 741–773.Google Scholar
Landahl, M. T. 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (02), 243–251.Google Scholar
Lee, M. & Moser, R. D. 2015 Direct numerical simulation of turbulent channel flow up to re5200. J. Fluid Mech. 774, 395–415.Google Scholar
Lemoult, G., Shi, L., Avila, K., Jalikop, S. V., Avila, M. & Hof, B. 2016 Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys. 12, 254–258.CrossRefGoogle Scholar
Marusic, I., Mathis, R. & Hutchins, N. 2010 Predictive model for wall-bounded turbulent flow. Science 329, 193–196.Google Scholar
Moin, P. & Kim, J. 1985 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.Google Scholar
Mösta, P., Ott, C. D., Radice, D., Roberts, L. F., Schnetter, E. & Haas, R. 2015 A large-scale dynamo and magnetoturbulence in rapidly rotating core-collapse supernovae. Nature 528, 376–379.CrossRefGoogle ScholarPubMed
Moum, J. N., Perlin, A., Nash, J. D. & Mcphaden, M. J. 2013 Seasonal sea surface cooling in the equatorial pacific cold tongue controlled by ocean mixing. Nature 500, 64–67.Google Scholar
Orr, W. M’F. 1907 The stability or instability of the steady motions of a perfect liquid and of a viscous liquid. Part ii: a viscous liquid. In Proceedings of the Royal Irish Academy. Section A: Mathematical and Physical Sciences, pp. 69–138. JSTOR.Google Scholar
Panton, R. L. 2001 Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37 (4), 341–383.CrossRefGoogle Scholar
Pringle, C. C. T., Willis, A. P. & Kerswell, R. R. 2012 Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos. J. Fluid Mech. 702, 415–443.CrossRefGoogle Scholar
Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21 (1), 015109.Google Scholar
Rabin, S. M. E., Caulfield, C. P. & Kerswell, R. R. 2012 Triggering turbulence efficiently in plane Couette flow. J. Fluid Mech. 712, 244–272.Google Scholar
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 (02), 263–288.CrossRefGoogle Scholar
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601–639.Google Scholar
Sano, M. & Tamai, K. 2016 A universal transition to turbulence in channel flow. Nat. Phys. 12, 249–253.Google Scholar
Schmid, P. J. & Henningson, D. S. 2012 Stability and Transition in Shear Flows, vol. 142. Springer.Google Scholar
Schoppa, W. & Hussain, F. 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57–108.Google Scholar
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 37–74.CrossRefGoogle Scholar
Townsend, A. A. 1980 The Structure of Turbulent Shear Flow. Cambridge University Press.Google Scholar
Viola, F., Iungo, G. V., Camarri, S., Port-Agel, F. & Gallaire, F. 2014 Prediction of the hub vortex instability in a wind turbine wake: stability analysis with eddy-viscosity models calibrated on wind tunnel data. J. Fluid Mech. 750, R1.Google Scholar
Waleffe, F. 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883–901.Google Scholar
Waleffe, F. 1998 Three-dimensional coherent states in plane shear flow. Phys. Rev. Lett. 81, 4140–4143.CrossRefGoogle Scholar
Wang, Y., Huang, W. & Xu, C. 2015 On hairpin vortex generation from near-wall streamwise vortices. Acta Mechanica Sin. 31 (2), 139–152.Google Scholar
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, 353–396.CrossRefGoogle Scholar