The influence of the secondary mean on linear analyses of turbulent square duct flow

Turbulent flow through square and rectangular ducts features Prandtl's secondary flow of the second kind, where the mean flow presents streamwise vortex pairs located near each corner. While the magnitude of these secondary flows are small (often a few percent of the streamwise component), here we show that they can have a substantial effect on stability and resolvent analyses of the mean-linearized system. In particular, the inclusion of such secondary mean components leads to the emergence of leading modes that are not otherwise present, particularly for streamwise-elongated structures. We show why such modes emerge mathematically, but through a comparison with direct numerical simulation data, argue that they are not necessarily physically relevant. When performing linear analyses with such secondary mean components removed, we instead can obtain leading (almost stationary) modes that resemble the secondary flow itself, potentially providing an alternative lens through which to study the emergence of such secondary flows. We lastly discuss the broader implications of these findings for other flows that feature secondary mean components.