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:
Revised:
Accepted:
Published online:
Frédéric Alizard 1
CC-BY 4.0
@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},
year = {2020},
publisher = {Acad\'emie des sciences, Paris},
volume = {348},
number = {12},
doi = {10.5802/crmeca.55},
language = {en},
}
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
[1] Bounds for threshold amplitudes in subcritical shear flows, J. Fluid Mech., Volume 270 (1994), pp. 175-198 | Zbl | MR | DOI
[2] On stability of streamwise streaks and transition thresholds in plane channel flows, J. Fluid Mech., Volume 365 (1998), pp. 269-303 | Zbl | MR | DOI
[3] A note on an algebraic instability of invscid parallel shear flow, J. Fluid Mech., Volume 98 (1980), pp. 243-251 | DOI
[4] Towards minimal perturbations in transitional plane Couette flow, Phys. Rev. E, Volume 82 (2010), 026316 | MR | DOI
[5] Subcritical transition in channel flows, J. Fluid Mech., Volume 451 (2002), pp. 35-97 | Zbl | MR | DOI
[6] Tracking stages of transition in Couette flow analytically, J. Fluid Mech., Volume 748 (2014), pp. 896-931 | DOI
[7] On the secondary instabilities of transient growth in Couette flow, J. Fluid Mech., Volume 813 (2017), pp. 528-557 | Zbl | MR | DOI
[8] Secondary threshold amplitudes for sinuous streak breakdown, Phys. Fluids, Volume 23 (2011), 074103 | DOI
[9] Edge of chaos in a parallel shear flow, Phys. Rev. Lett., Volume 96 (2006), 174101
[10] Nonequlibrium thermodynamics and the optimal path to turbulence in shear flows, Phys. Rev. Lett., Volume 106 (2011), 134502 | DOI
[11] Triggering turbulence efficiently in plane Couette flow, J. Fluid Mech., Volume 712 (2012), pp. 244-272 | Zbl | MR | DOI
[12] Minimal transition thresholds in plane Couette flow, Phys. Fluids, Volume 25 (2013), 084103 | DOI
[13] Nonlinear nonmodal stability theory, Annu. Rev. Fluid Mech., Volume 50 (2018), pp. 319-345 | Zbl | MR | DOI
[14] On strongly nonlinear vortex/wave interactions in boundary-layer transition, J. Fluid Mech., Volume 227 (1991), pp. 641-666 | Zbl | DOI
[15] The emergence of localized vortex-wave interaction states in plane Couette flow, J. Fluid Mech., Volume 721 (2013), pp. 58-85 | MR | DOI
[16] Self-sustained states at Kolmogorov microscale, J. Fluid Mech., Volume 781 (2015), p. R6 | Zbl | MR | DOI
[17] Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech., Volume 287 (1995), pp. 317-348 | Zbl | DOI
[18] Lower branch coherent states in shear flows: transition and control, Phys. Rev. Lett., Volume 98 (2007), 204501 | DOI
[19] An optimal path to transition in a duct, Phil. Trans. R. Soc., Volume 367 (2009), pp. 529-544 | Zbl | MR | DOI
[20] Dynamics of streamwise rolls and streaks in turbulent wall-bounded shear flow, J. Fluid Mech., Volume 708 (2012), pp. 149-196 | Zbl | MR | DOI
[21] Weakly nonlinear optimal perturbations, J. Fluid Mech., Volume 785 (2015), pp. 135-151 | Zbl | MR | DOI
[22] Linear stability of optimal streaks in the log-layer of turbulent channel flows, Phys. Fluids, Volume 27 (2015), 105103 | DOI
[23] Invariant solutions in a channel flow using a minimal restricted nonlinear model, C. R. Méc., Volume 345 (2017), pp. 117-124 | DOI
[24] Stability and Transition in Shear Flows, Applied Mathematical Sciences, vol. 142, Springer-Verlag, New York, 2001 | Zbl
[25] Using nonlinear transient growth to construct the minimal seed for shear flow turbulence, Phys. Rev. Lett., Volume 105 (2010), 154502
Cited by Sources:
Comments - Policy