Travelling-waves consistent with turbulence-driven secondary flow in a square duct

TL;DR

This paper numerically identifies travelling-wave solutions in square duct flow that resemble turbulence-driven secondary flows, revealing coherent structures similar to those observed in turbulence.

Contribution

It introduces a new family of travelling-wave solutions that replicate the secondary flow patterns seen in turbulent square duct flow.

Findings

Solutions exhibit coherent vortex structures

Flow patterns match turbulent secondary flow

Reveals link between travelling waves and turbulence

Abstract

We present numerically determined travelling-wave solutions for pressure-driven flow through a straight duct with a square cross-section. This family of solutions represents typical coherent structures (a staggered array of counter-rotating streamwise vortices and an associated low-speed streak) on each wall. Their streamwise average flow in the cross-sectional plane corresponds to an eight vortex pattern much alike the secondary flow found in the turbulent regime.