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

Subhandu Rawat; Carlo Cossu; François Rincon

doi:10.1016/j.crme.2015.12.005

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

Subhandu 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, 31400 Toulouse, France
³ CNRS, IRAP, 14, avenue Édouard-Belin, 31400 Toulouse, France

Comptes Rendus. Mécanique, Volume 344 (2016) no. 6, pp. 448-455.

Abstract

Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at $Re = 2000$ in a saddle-node infinite-period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi-streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size $L_{z}$ of the domain in which they are computed is increased. On the contrary, the upper branch of travelling-wave solutions develops multiple streaks when $L_{z}$ is increased. Upper-branch travelling-wave solutions can be continued into coherent solutions to the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.

Received: 2015-07-04
Accepted: 2015-12-28
Published online: 2016-03-19

DOI: 10.1016/j.crme.2015.12.005

Keywords: Fluid dynamics, Hydrodynamic stability, Transition to turbulence

Author's affiliations:

Subhandu 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, 31400 Toulouse, France
³ CNRS, IRAP, 14, avenue Édouard-Belin, 31400 Toulouse, France

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     title = {Travelling-wave solutions bifurcating from relative periodic orbits in plane {Poiseuille} flow},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {448--455},
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     volume = {344},
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     doi = {10.1016/j.crme.2015.12.005},
     language = {en},
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Subhandu Rawat; Carlo Cossu; François Rincon. Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow. Comptes Rendus. Mécanique, Volume 344 (2016) no. 6, pp. 448-455. doi : 10.1016/j.crme.2015.12.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2015.12.005/

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