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

TL;DR

This paper demonstrates the bifurcation of travelling-wave solutions from relative periodic orbits in plane Poiseuille flow at Re=2000, revealing their structure, evolution with domain size, and relevance to turbulent motions.

Contribution

It identifies and characterizes travelling-wave solutions bifurcating from relative periodic orbits, linking them to turbulent large-scale motions in plane Poiseuille flow.

Findings

Travelling-wave solutions bifurcate at Re=2000 in a saddle-node infinite period bifurcation.

Lower branch solutions become spanwise localized as domain size increases.

Upper branch solutions develop multiple streaks and relate to turbulent motions.

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 Lz of the domain in which they are computed is increased. On the contrary, upper branch of travelling-wave solutions develop multiple streaks when Lz is increased. Upper branch travelling-wave solutions can be continued into coherent solutions of the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.