Comptes Rendus
no. 2
Invariant solutions in a channel flow using a minimal restricted nonlinear model
Frédéric Alizard1, 2 
1 LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, France
2 DynFluid–CNAM, 151, boulevard de l'Hôpital, 75013 Paris, France
Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 117-124.

Simulations using a Restricted Nonlinear (RNL) system, where mean flow distortion resulting from Reynolds stress feedback regenerates rolls, is applied in a channel flow under subcritical conditions. This quasi-linear restriction of the dynamics is used to study invariant solutions located in the bulk of the flow found recently by Rawat et al. (2016) [14]. It is shown that the RNL system truncated to a single streamwise mode for the perturbation supports invariant solutions that are found to bifurcate from a relative periodic orbit into a travelling wave solution when the spanwise size is increasing. In particular, the travelling wave solution exhibits a spanwise localized structure that remains unchanged for large values of the spanwise extent as the invariant solution lying on the lower branch found by Rawat et al. (2016) [14]. In addition, travelling wave solutions provided by this minimal RNL system are self-similar with respect to the Reynolds number based on the centreline velocity, and the half-channel height varying from 2000 to 5000.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2016.11.005
Mots clés : Channel flow, Invariant solutions, Subcritical transition
Frédéric Alizard 1, 2

1 LMFA, CNRS, Ecole Centrale de Lyon, Université Lyon 1, INSA Lyon, France
2 DynFluid–CNAM, 151, boulevard de l'Hôpital, 75013 Paris, France 
@article{CRMECA_2017__345_2_117_0,
     author = {Fr\'ed\'eric Alizard},
     title = {Invariant solutions in a channel flow using a minimal restricted nonlinear model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {117--124},
     publisher = {Elsevier},
     volume = {345},
     number = {2},
     year = {2017},
     doi = {10.1016/j.crme.2016.11.005},
     language = {en},
}
TY  - JOUR
AU  - Frédéric Alizard
TI  - Invariant solutions in a channel flow using a minimal restricted nonlinear model
JO  - Comptes Rendus. Mécanique
PY  - 2017
SP  - 117
EP  - 124
VL  - 345
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2016.11.005
LA  - en
ID  - CRMECA_2017__345_2_117_0
ER  - 
%0 Journal Article
%A Frédéric Alizard
%T Invariant solutions in a channel flow using a minimal restricted nonlinear model
%J Comptes Rendus. Mécanique
%D 2017
%P 117-124
%V 345
%N 2
%I Elsevier
%R 10.1016/j.crme.2016.11.005
%G en
%F CRMECA_2017__345_2_117_0
Frédéric Alizard. Invariant solutions in a channel flow using a minimal restricted nonlinear model. Comptes Rendus. Mécanique, Volume 345 (2017) no. 2, pp. 117-124. doi : 10.1016/j.crme.2016.11.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.11.005/

[1] Y. Duguet; C.C.T. Pringle; R.R. Kerswell Relative periodic orbits in transitional pipe flow, Phys. Fluids, Volume 11 (2008)

[2] R.R. Kerswell; O. Tutty Recurrence of travelling wave solutions in transitional pipe flow, J. Fluid Mech., Volume 584 (2007), pp. 69-102

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

[4] T.M. Schneider; D. Marinc; B. Eckhard Localized edge states nucleate turbulence in extended plane Couette cells, J. Fluid Mech., Volume 646 (2010), pp. 441-451

[5] G. Kawara; M. Uhlmann; L. Van Veen The significance of simple invariant solutions in turbulent flows, Annu. Rev. Fluid Mech., Volume 44 (2012), pp. 203-225

[6] J. Jimenéz; M. Simens Low-dimensional dynamics of a turbulent wall flow, J. Fluid Mech., Volume 435 (2001), pp. 81-91

[7] J.F. Gibson; E. Brand Spanwise-localized solutions of planar shear flows, J. Fluid Mech., Volume 745 (2014), pp. 25-61

[8] J. Jimenéz; P. Moin The minimal flow unit in near-wall turbulence, J. Fluid Mech., Volume 225 (1991), pp. 213-240

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

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

[11] F. Waleffe; J. Kim How streamwise rolls and streaks self-sustain in a shear flow (R. Panton, ed.), Computational Mechanics Publications, 1997, pp. 309-332

[12] 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)

[13] S. Rawat; C. Cossu; F. Rincon Relative periodic orbits in plane Poiseuille flow, C. R. Mecanique, Volume 342 (2014), pp. 485-489

[14] S. Rawat; C. Cossu; F. Rincon Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow, C. R. Mecanique, Volume 344 (2016), pp. 448-455

[15] Y. Hwang; A.P. Willis; C. Cossu Invariant solutions of minimal large-scale structures in turbulent channel flow for Reτ up to 1000, J. Fluid Mech., Volume 802 (2016)

[16] V.L. Thomas; B.F. Farrell; P.J. Ioannou; D.F. Gayme A minimal model of self-sustaining turbulence, Phys. Fluids, Volume 27 (2015)

[17] B.F. Farrell; P.J. Ioannou; J. Jiménez; N.C. Constantinou; A. Lozano-Durán; M.-A. Nikolaidis A statistical state dynamics based study of the structure and mechanism of large-scale motions in plane Poiseuille flow, J. Fluid Mech., Volume 809 (2016), pp. 290-315

[18] D. Biau; A. Bottaro An optimal path to transition in a duct, Philos. Trans. R. Soc. A, Volume 367 (2009), pp. 529-544

[19] J.O. Pralits; A. Bottaro; S. Cherubini Weakly nonlinear optimal perturbations, J. Fluid Mech., Volume 785 (2015), pp. 135-151

[20] V. Mantic-Lugo; C. Arratia; F. Gallaire Self-consistent mean flow description of the nonlinear saturation of the vortex shedding in the cylinder wake, Phys. Rev. Lett., Volume 113 (2014)

[21] S.E. Turton; L.S. Tuckerman; D. Barkley Prediction of frequencies in thermosolutal convection from mean flows, Phys. Rev. E, Volume 91 (2015)

[22] F. Alizard Linear stability of optimal streaks in the log-layer of turbulent channel flows, Phys. Fluids, Volume 27 (2015)

[23] R. Peyret Spectral Methods for Incompressible Viscous Flow, Springer, 2002

[24] W. Schoppa; F. Hussain Coherent structure generation in near-wall turbulence, J. Fluid Mech., Volume 453 (2002), pp. 57-108

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

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow

Subhandu Rawat; Carlo Cossu; François Rincon

C. R. Méca (2016)

Relative periodic orbits in plane Poiseuille flow

Subhendu Rawat; Carlo Cossu; François Rincon

C. R. Méca (2014)

On the stability of large-scale streaks in turbulent Couette and Poiseulle flows

Junho Park; Yongyun Hwang; Carlo Cossu

C. R. Méca (2011)