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Optimal bursts in turbulent channel flow

  • Mirko Farano (a1) (a2), Stefania Cherubini (a1) (a2), Jean-Christophe Robinet (a2) and Pietro De Palma (a1)

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.

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R. J. Adrian 2007 Hairpin vortex organization in wall turbulence. Phys. Fluids 19 (4), 041301.

R. J. Adrian , S. Balachandar  & Z. C. Lin 2001 Spanwise growth of vortex structure in wall turbulence. KSME Intl J. 15 (12), 17411749.

J. C. del Álamo  & J. Jiménez 2003 Spectra of the very large anisotropic scales in turbulent channels. Phys. Fluids 15 (6), L41.

P. Andersson , L. Brandt , A. Bottaro  & D. S. Henningson 2001 On the breakdown of boundary layer streaks. J. Fluid Mech. 428, 2960.

D. Barkley , B. Song , V. Mukund , G. Lemoult , M. Avila  & B. Hof 2015 The rise of fully turbulent flow. Nature 526, 550553.

H. M. Blackburn , N. N. Mansour  & B. J. Cantwell 1996 Topology of fine-scale motions in turbulent channel flow. J. Fluid Mech. 310, 269292.

D. G. Bogard  & W. G. Tiederman 1986 Burst detection with single-point velocity measurements. J. Fluid Mech. 162, 389413.

K. M. Butler  & B. F. Farrell 1993 Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids A 5 (3), 774777.

S. Cherubini , P. De Palma  & J.-C. Robinet 2015 Nonlinear optimals in the asymptotic suction boundary layer: transition thresholds and symmetry breaking. Phys. Fluids 27 (3), 034108.

M. S. Chong , A. E. Perry  & B. J. Cantwell 1990 A general classification of three-dimensional flow fields. Phys. Fluids A 2 (5), 765777.

C. Cossu , G. Pujals  & S. Depardon 2009 Optimal transient growth and very large-scale structures in turbulent boundary layers. J. Fluid Mech. 619, 7994.

M. O. Deville , P. F. Fischer  & E. H. Mund 2002 High-Order Methods for Incompressible Fluid Flow, vol. 9. Cambridge University Press.

Y. Duguet , A. Monokrousos , L. Brandt  & D. S. Henningson 2013 Minimal transition thresholds in plane Couette flow. Phys. Fluids 25 (8), 084103.

G. Eitel-Amor , R. Örlü , P. Schlatter  & O. Flores 2015 Hairpin vortices in turbulent boundary layers. Phys. Fluids 27 (2), 025108.

H. Faisst  & B. Eckhardt 2003 Travelling waves in pipe flow. Phys. Rev. Lett. 91, 224502.

M. Farano , S. Cherubini , J.-C. Robinet  & P. De Palma 2015 Hairpin-like optimal perturbations in plane poiseuille flow. J. Fluid Mech. 775, R2.

M. Farano , S. Cherubini , J.-C. Robinet  & P. De Palma 2016 Subcritical transition scenarios via linear and nonlinear localized optimal perturbations in plane poiseuille flow. Fluid Dyn. Res. 48, 061409.

O. Flores  & J. Jimenez 2010 Hierarchy of minimal flow units in the logarithmic layer. Phys. Fluids 22, 071704.

J. M. Hamilton , J. Kim  & F. Waleffe 1995 Regeneration mechanisms of near-wall turbulence structures. J. Fluid Mech. 287, 317348.

D. K. Heist , T. J. Hanratty  & Y. Na 2000 Observations of the formation of streamwise vortices by rotation of arch vortices. Phys. Fluids 12 (11), 29652975.

B. Hof , C. W. H. van Doorne , J. Westerweel , F. T. M. Nieuwstadt , H. Faisst , B. Eckhardt , H. Wedin , R. R. Kerswell  & F. Waleffe 2004 Experimental observation of nonlinear traveling waves in turbulent pipe flow. Science 305, 15941598.

J. Hwang , J. Lee , H. J. Sung  & T. A. Zaki 2016 Inner–outer interactions of large-scale structures in turbulent channel flow. J. Fluid Mech. 790, 128157.

Y. Hwang  & C. Cossu 2010b Self-sustained process at large scales in turbulent channel flow. Phys. Rev. Lett. 105 (4), 044505.

J. Jiménez 1999 The physics of wall turbulence. Physica A 263 (1), 252262.

J. Jiménez 2013 How linear is wall-bounded turbulence? Phys. Fluids 25, 110814.

J. Jiménez 2015 Direct detection of linearized bursts in turbulence. Phys. Fluids 27, 065102.

J. Jiménez  & P. Moin 1991 The minimal flow unit in near-wall turbulence. J. Fluid Mech. 225, 213240.

J. J. Jiménez , G. Kawahara , M. P. Simens , N. Nagata  & M. Shiba 2005 Characterization of near-wall turbulence in terms of equilibrium and bursting solutions. Phys. Fluids 17, 015105.

J. J. Jiménez  & A. Pinelli 1999 The autonomous cycle of near-wall turbulence. J. Fluid Mech. 389, 335359.

J. Kim , P. Moin  & R. Moser 1987 Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177, 133166.

S. J. Kline , W. C. Reynold , F. Schraub  & P. W. Rundstander 1967 The structure of turbulent boundary layer flows. J. Fluid Mech. 30, 741773.

M. T. Landahl 1980 A note on an algebraic instability of inviscid parallel shear flows. J. Fluid Mech. 98 (02), 243251.

G. Lemoult , L. Shi , K. Avila , S. V. Jalikop , M. Avila  & B. Hof 2016 Directed percolation phase transition to sustained turbulence in Couette flow. Nat. Phys. 12, 254258.

I. Marusic , R. Mathis  & N. Hutchins 2010 Predictive model for wall-bounded turbulent flow. Science 329, 193196.

P. Moin  & J. Kim 1985 The structure of the vorticity field in turbulent channel flow. Part 1. Analysis of instantaneous fields and statistical correlations. J. Fluid Mech. 155, 441464.

P. Mösta , C. D. Ott , D. Radice , L. F. Roberts , E. Schnetter  & R. Haas 2015 A large-scale dynamo and magnetoturbulence in rapidly rotating core-collapse supernovae. Nature 528, 376379.

J. N. Moum , A. Perlin , J. D. Nash  & M. J. Mcphaden 2013 Seasonal sea surface cooling in the equatorial pacific cold tongue controlled by ocean mixing. Nature 500, 6467.

R. L. Panton 2001 Overview of the self-sustaining mechanisms of wall turbulence. Prog. Aerosp. Sci. 37 (4), 341383.

G. Pujals , M. García-Villalba , C. Cossu  & S. Depardon 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21 (1), 015109.

W. C. Reynolds  & A. K. M. F. Hussain 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (02), 263288.

S. K. Robinson 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23 (1), 601639.

M. Sano  & K. Tamai 2016 A universal transition to turbulence in channel flow. Nat. Phys. 12, 249253.

W. Schoppa  & F. Hussain 2002 Coherent structure generation in near-wall turbulence. J. Fluid Mech. 453, 57108.

C. D. Tomkins  & R. J. Adrian 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.

F. Waleffe 1997 On a self-sustaining process in shear flows. Phys. Fluids 9, 883901.

F. Waleffe 1998 Three-dimensional coherent states in plane shear flow. Phys. Rev. Lett. 81, 41404143.

Y. Wang , W. Huang  & C. Xu 2015 On hairpin vortex generation from near-wall streamwise vortices. Acta Mechanica Sin. 31 (2), 139152.

J. Zhou , R. J. Adrian , S. Balachandar  & T. M. Kendall 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353396.

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