Comptes Rendus
Relative periodic orbits in plane Poiseuille flow
Comptes Rendus. Mécanique, Volume 342 (2014) no. 8, pp. 485-489.

A branch of relative periodic orbits is found in plane Poiseuille flow in a periodic domain at Reynolds numbers ranging from Re=3000 to Re=5000. These solutions consist in sinuous quasi-streamwise streaks periodically forced by quasi-streamwise vortices in a self-sustained process. The streaks and the vortices are located in the bulk of the flow. Only the amplitude, but not the shape, of the averaged velocity components does change as the Reynolds number is increased from 3000 to 5000. We conjecture that these solutions could therefore be related to large- and very large-scale structures observed in the bulk of fully developed turbulent channel flows.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2014.05.008
Keywords: Fluid dynamics, Hydrodynamic stability, Transition to turbulence

Subhendu Rawat 1; Carlo Cossu 1; François Rincon 2, 3

1 Institut de mécanique des fluides de Toulouse, CNRS and Université de Toulouse, allée du Professeur-Camille-Soula, 31400 Toulouse, France
2 Université de Toulouse, UPS–OMP, IRAP, Toulouse, France
3 CNRS, IRAP, 14, avenue Édouard-Belin, 31400 Toulouse, France
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Subhendu Rawat; Carlo Cossu; François Rincon. Relative periodic orbits in plane Poiseuille flow. Comptes Rendus. Mécanique, Volume 342 (2014) no. 8, pp. 485-489. doi : 10.1016/j.crme.2014.05.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.05.008/

[1] R. Artuso; E. Aurell; P. Cvitanovic Recycling of strange sets: I. Cycle expansions, Nonlinearity, Volume 3 (1990), p. 325

[2] T.R. Bewley Numerical Renaissance: Simulation, Optimization and Control, Renaissance Press, San Diego, CA, USA, 2008

[3] R.M. Clever; F.H. Busse Three-dimensional convection in a horizontal fluid layer subjected to a constant shear, J. Fluid Mech., Volume 234 (1992), pp. 511-527

[4] R.M. Clever; F.H. Busse Tertiary and quaternary solutions for plane Couette flow, J. Fluid Mech., Volume 344 (1997), pp. 137-153

[5] C. Cossu; M. Chevalier; D.S. Henningson Secondary optimal growth and subcritical transition in the plane Poiseuille flow (P. Schlatter; D.S. Henningson, eds.), Seventh IUTAM Symposium on Laminar–Turbulent Transition, Springer, 2010, pp. 129-134

[6] C. Cossu; L. Brandt; S. Bagheri; D.S. Henningson Secondary threshold amplitudes for sinuous streak breakdown, Phys. Fluids, Volume 23 (2011), p. 074103

[7] Y. Duguet; C.C.T. Pringle; R.R. Kerswell Relative periodic orbits in transitional pipe flow, Phys. Fluids, Volume 20 (2008) no. 11, p. 114102

[8] T. Duriez; J.-L. Aider; J.E. Wesfreid Self-sustaining process through streak generation in a flat-plate boundary layer, Phys. Rev. Lett., Volume 103 (2009), p. 144502

[9] U. Ehrenstein; W. Koch Three-dimensional wavelike equilibrium states in plane Poiseuille flow, J. Fluid Mech., Volume 228 (1991), pp. 111-148

[10] H. Faisst; B. Eckhardt Travelling waves in pipe flow, Phys. Rev. Lett., Volume 91 (2003), p. 24502

[11] J.F. Gibson; J. Halcrow; P. Cvitanovic Visualizing the geometry of state space in plane Couette flow, J. Fluid Mech., Volume 611 (2008), pp. 107-130

[12] M. Guala; S.E. Hommema; R.J. Adrian Large-scale and very-large-scale motions in turbulent pipe flow, J. Fluid Mech., Volume 554 (2006), pp. 521-541

[13] J.M. Hamilton; J. Kim; F. Waleffe Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech., Volume 287 (1995), pp. 317-348

[14] J. Herault; F. Rincon; C. Cossu; G. Lesur; G.I. Ogilvie; P.-Y. Longaretti Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic field generation in shear flows, Phys. Rev. E, Volume 84 (2011), p. 036321

[15] Y. Hwang; C. Cossu Self-sustained process at large scales in turbulent channel flow, Phys. Rev. Lett., Volume 105 (2010) no. 4 (044505)

[16] Y. Hwang; C. Cossu Self-sustained processes in the logarithmic layer of turbulent channel flows, Phys. Fluids, Volume 23 (2011) (061702)

[17] T. Itano; S. Toh The dynamics of bursting process in wall turbulence, J. Phys. Soc. Jpn., Volume 70 (2001), pp. 703-716

[18] G. Kawahara; S. Kida Periodic motion embedded in plane Couette turbulence: regeneration cycle and burst, J. Fluid Mech., Volume 449 (2001), pp. 291-300

[19] R.R. Kerswell; O.R. Tutty Recurrence of traveling waves in transitional pipe flow, J. Fluid Mech., Volume 584 (2007), pp. 69-102

[20] K.C. Kim; R. Adrian Very large-scale motion in the outer layer, Phys. Fluids, Volume 11 (1999) no. 2, pp. 417-422

[21] L.S.G. Kovasznay; V. Kibens; R.F. Blackwelder Large-scale motion in the intermittent region of a turbulent boundary layer, J. Fluid Mech., Volume 41 (1970), pp. 283-325

[22] T. Kreilos; B. Eckhardt Periodic orbits near onset of chaos in plane Couette flow, Chaos, Volume 22 (2012) no. 4, p. 047505

[23] T. Kreilos; G. Veble; T.M. Schneider; B. Eckhardt Edge states for the turbulence transition in the asymptotic suction boundary layer, J. Fluid Mech., Volume 726 (2013), pp. 100-122

[24] M. Nagata Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity, J. Fluid Mech., Volume 217 (1990), pp. 519-527

[25] A. Riols; F. Rincon; C. Cossu; G. Lesur; P.-Y. Longaretti; G.I. Ogilvie; J. Herault Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow, J. Fluid Mech., Volume 731 (2013), pp. 1-45

[26] T.M. Schneider; B. Eckhardt; J. Vollmer Statistical analysis of coherent structures in transitional pipe flow, Phys. Rev. E, Volume 75 (2007), p. 066313

[27] S. Toh; T. Itano A periodic-like solution in channel flow, J. Fluid Mech., Volume 481 (2003), pp. 67-76

[28] D. Viswanath The dynamics of transition to turbulence in plane couette flow, 2007 | arXiv

[29] F. Waleffe Three-dimensional coherent states in plane shear flows, Phys. Rev. Lett., Volume 81 (1998), pp. 4140-4143

[30] F. Waleffe Homotopy of exact coherent structures in plane shear flows, Phys. Fluids, Volume 15 (2003), pp. 1517-1534

[31] H. Wedin; R.R. Kerswell Exact coherent structures in pipe flow: traveling wave solutions, J. Fluid Mech., Volume 508 (2004), pp. 333-371

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