Oblique and streamwise vortex paths in a plane Couette flow using a RNL system

Frédéric Alizard

doi:10.5802/crmeca.55

Note

Oblique and streamwise vortex paths in a plane Couette flow using a RNL system

Frédéric Alizard ¹

¹ LMFA, UMR 5509, Univ Lyon, Université Claude Bernard Lyon 1, École Centrale de Lyon, INSA Lyon, CNRS, 43 Boulevard du 11 Novembre 1918, F-69100, Villeurbanne, France

Comptes Rendus. Mécanique, Volume 348 (2020) no. 12, pp. 959-968.

Résumé

This paper revisits oblique wave and streamwise vortex scenarios in a plane Couette flow using restricted nonlinear simulations, where only a single Fourier mode for perturbation is retained. It is shown that this restriction of full dynamics gives a good approximation of the two subcritical paths. In particular, critical energy thresholds and edge states compare favorably with results obtained using direct numerical simulations by Duguet et al. (Phys. Rev. E 82 (2010), 026316).

Supplementary Materials:
Supplementary material for this article is supplied as a separate file:

crmeca-55-suppl.zip

Reçu le : 2020-07-15
Révisé le : 2020-10-08
Accepté le : 2020-10-13
Publié le : 2021-01-19

DOI : 10.5802/crmeca.55

Mots clés : Shear flows, Subcritical transition, Reduced order model, Edge states, Plane Couette flow

Affiliations des auteurs :

Frédéric Alizard ¹

¹ LMFA, UMR 5509, Univ Lyon, Université Claude Bernard Lyon 1, École Centrale de Lyon, INSA Lyon, CNRS, 43 Boulevard du 11 Novembre 1918, F-69100, Villeurbanne, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRMECA_2020__348_12_959_0,
     author = {Fr\'ed\'eric Alizard},
     title = {Oblique and streamwise vortex paths in a plane {Couette} flow using a {RNL} system},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {959--968},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {348},
     number = {12},
     year = {2020},
     doi = {10.5802/crmeca.55},
     language = {en},
}

TY  - JOUR
AU  - Frédéric Alizard
TI  - Oblique and streamwise vortex paths in a plane Couette flow using a RNL system
JO  - Comptes Rendus. Mécanique
PY  - 2020
SP  - 959
EP  - 968
VL  - 348
IS  - 12
PB  - Académie des sciences, Paris
DO  - 10.5802/crmeca.55
LA  - en
ID  - CRMECA_2020__348_12_959_0
ER  -

%0 Journal Article
%A Frédéric Alizard
%T Oblique and streamwise vortex paths in a plane Couette flow using a RNL system
%J Comptes Rendus. Mécanique
%D 2020
%P 959-968
%V 348
%N 12
%I Académie des sciences, Paris
%R 10.5802/crmeca.55
%G en
%F CRMECA_2020__348_12_959_0

Frédéric Alizard. Oblique and streamwise vortex paths in a plane Couette flow using a RNL system. Comptes Rendus. Mécanique, Volume 348 (2020) no. 12, pp. 959-968. doi : 10.5802/crmeca.55. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.55/

Bibliographie
Cité par

[1] G. Kreiss; A. Lundbladh; D. S. Henningson Bounds for threshold amplitudes in subcritical shear flows, J. Fluid Mech., Volume 270 (1994), pp. 175-198 | DOI | MR | Zbl

[2] S. Reddy; P. Schmid; J. Baggett; D. S. Henningson On stability of streamwise streaks and transition thresholds in plane channel flows, J. Fluid Mech., Volume 365 (1998), pp. 269-303 | DOI | MR | Zbl

[3] M. T. Landhal A note on an algebraic instability of invscid parallel shear flow, J. Fluid Mech., Volume 98 (1980), pp. 243-251 | DOI

[4] Y. Duguet; L. Brandt; B. R. J. Larson Towards minimal perturbations in transitional plane Couette flow, Phys. Rev. E, Volume 82 (2010), 026316 | DOI | MR

[5] S. J. Chapman Subcritical transition in channel flows, J. Fluid Mech., Volume 451 (2002), pp. 35-97 | DOI | MR | Zbl

[6] M. Karp; J. Cohen Tracking stages of transition in Couette flow analytically, J. Fluid Mech., Volume 748 (2014), pp. 896-931 | DOI

[7] M. Karp; J. Cohen On the secondary instabilities of transient growth in Couette flow, J. Fluid Mech., Volume 813 (2017), pp. 528-557 | DOI | MR | Zbl

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

[9] J. D. Skufca; J. A. Yorke; B. Eckhardt Edge of chaos in a parallel shear flow, Phys. Rev. Lett., Volume 96 (2006), 174101

[10] A. Monokrousos; A. Bottaro; L. Brandt; A. Di Vita; D. S. Henningson Nonequlibrium thermodynamics and the optimal path to turbulence in shear flows, Phys. Rev. Lett., Volume 106 (2011), 134502 | DOI

[11] S. M. E. Rabin; C. P. Caulfield; R. R. Kerswell Triggering turbulence efficiently in plane Couette flow, J. Fluid Mech., Volume 712 (2012), pp. 244-272 | DOI | MR | Zbl

[12] Y. Duguet; A. Monokrousos; L. Brandt Minimal transition thresholds in plane Couette flow, Phys. Fluids, Volume 25 (2013), 084103 | DOI

[13] R. R. Kerswell Nonlinear nonmodal stability theory, Annu. Rev. Fluid Mech., Volume 50 (2018), pp. 319-345 | DOI | MR | Zbl

[14] P. Hall; F. T. Smith On strongly nonlinear vortex/wave interactions in boundary-layer transition, J. Fluid Mech., Volume 227 (1991), pp. 641-666 | DOI | Zbl

[15] K. Deguchi; P. Hall; A. G. Watson The emergence of localized vortex-wave interaction states in plane Couette flow, J. Fluid Mech., Volume 721 (2013), pp. 58-85 | DOI | MR

[16] K. Deguchi Self-sustained states at Kolmogorov microscale, J. Fluid Mech., Volume 781 (2015), p. R6 | DOI | MR | Zbl

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

[18] J. Wang; J. Gibson; F. Waleffe Lower branch coherent states in shear flows: transition and control, Phys. Rev. Lett., Volume 98 (2007), 204501 | DOI

[19] D. Biau; A. Bottaro An optimal path to transition in a duct, Phil. Trans. R. Soc., Volume 367 (2009), pp. 529-544 | DOI | MR | Zbl

[20] B. F. Farrell; P. J. Ioannou Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow, J. Fluid Mech., Volume 708 (2012), pp. 149-196 | DOI | MR | Zbl

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

[22] F. Alizard Linear stability of optimal streaks in the log-layer of turbulent channel flows, Phys. Fluids, Volume 27 (2015), 105103 | DOI

[23] F. Alizard Invariant solutions in a channel flow using a minimal restricted nonlinear model, C. R. Méc., Volume 345 (2017), pp. 117-124 | DOI

[24] P. J. Schmid; D. S. Henningson Stability and Transition in Shear Flows, Applied Mathematical Sciences, vol. 142, Springer-Verlag, New York, 2001 | Zbl

[25] C. C. T. Pringle; R. R. Kerswell Using nonlinear transient growth to construct the minimal seed for shear flow turbulence, Phys. Rev. Lett., Volume 105 (2010), 154502

Cité par Sources :

Commentaires - Politique