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

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.

References in corpus (3)

• Visualizing the geometry of state space in plane Couette flow
• Lower branch coherent states in shear flows: transition and control
• The critical layer in pipe flow at high Reynolds number

Cited by in corpus (8)

• The Significance of Simple Invariant Solutions in Turbulent Flows
• Spatially localized solutions of shear flows
• Koopman mode expansions between simple invariant solutions
• On the role of turbulent large-scale streaks in generating sediment ridges
• Periodically bursting edge states in plane Poiseuille flow
• New equilibrium solution branches of plane Couette flow discovered using a project-then-search method
• Energy stability of magnetohydrodynamic flow in channels and ducts
• Can preferential concentration of finite-size particles in plane Couette turbulence be reproduced with the aid of equilibrium solutions?