Travelling waves in a straight square duct

Abstract

Isothermal, incompressible flow in a straight duct with square cross-section is known to be linearly stable [1]. Direct numerical simulation, on the other hand, has revealed that turbulence in this geometry is self-sustained above a Reynolds number value of approximately 1100, based on the bulk velocity and the duct half-width [2]. Numerous non-linear equilibrium solutions have already been identified in plane Couette, plane Poiseuille and pipe flows [3, 4, 5], and their role in the transition process as well as their relevance to the statistics of turbulent flow have been investigated [6, 7, 8]. No non-linear travelling-wave solutions for the flow through a square duct have been published to date.