Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?

TL;DR

This paper investigates the nonlinear dynamics of plane Poiseuille flow turbulence at Re=3000, identifying a traveling-wave solution that acts as a saddle point influencing the flow's evolution and transition to turbulence.

Contribution

It reveals a localized traveling-wave solution in plane Poiseuille flow that resembles experimental structures and analyzes its saddle point phase space structure.

Findings

The TWS is localized near one wall and resembles observed coherent structures.

The phase space around TWS acts like a saddle point with stable and unstable manifolds.

Bursting corresponds to escape from the TWS along its unstable manifold.

Abstract

The instability of a streak and its nonlinear evolution are investigated by direct numerical simulation (DNS) for plane Poiseuille flow at Re=3000. It is suggested that there exists a traveling-wave solution (TWS). The TWS is localized around one of the two walls and notably resemble to the coherent structures observed in experiments and DNS so far. The phase space structure around this TWS is similar to a saddle point. Since the stable manifold of this TWS is extended close to the quasi two dimensional (Q2D) energy axis, the approaching process toward the TWS along the stable manifold is approximately described as the instability of the streak (Q2D flow) and the succeeding nonlinear evolution. Bursting corresponds to the escape from the TWS along the unstable manifold. These manifolds constitute part of basin boundary of the turbulent state.