Unstable periodic orbits and heteroclinic connections in plane Couette flow

TL;DR

This paper explores the invariant solutions such as periodic orbits and heteroclinic connections in plane Couette flow, providing visualizations that enhance understanding of turbulent shear flows as dynamical systems.

Contribution

It introduces precise computation of invariant solutions in plane Couette flow at high Reynolds numbers and visualizes their relation to turbulence dynamics.

Findings

Visualization of periodic orbits in plane Couette flow

Identification of heteroclinic connections between unstable equilibria

Turbulent flow passing close to computed periodic orbits

Abstract

Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of wall-bounded rolls and streaks and provide a framework for understanding low-Reynolds turbulent shear flows as dynamical systems. We present fluid dynamics videos of plane Couette flow illustrating periodic orbits, a close pass of turbulent flow to a periodic orbit, and heteroclinic connections between unstable equilibria.