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

Subhandu Rawat (1) , Carlo Cossu (1) , François Rincon (2)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 IRAP - Institut de recherche en astrophysique et planétologie

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.

Mots clés: Fluid dynamics; Hydrodynamic stability; Transition to turbulence

Domaines: Mécanique des fluides [physics.class-ph]

Subhandu Rawat, Carlo Cossu, François Rincon. Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow. Comptes Rendus Mécanique, 2016, vol. 344 (n° 6), pp. 448-455. ⟨10.1016/j.crme.2015.12.005⟩. ⟨hal-01557352⟩