  This research focuses on the identification and causality analysis of
coherent structures that arise in turbulent flows in square and rectangular
ducts. Coherent structures are first identified from direct numerical
simulation data via proper orthogonal decomposition (POD), both by using all
velocity components, and after separating the streamwise and secondary
components of the flow. The causal relations between the mode coefficients are
analysed using pairwise-conditional Granger causality analysis. We also
formulate a nonlinear Granger causality analysis that can account for nonlinear
interactions between modes. Focusing on streamwise-constant structures within a
duct of short streamwise extent, we show that the causal relationships are
highly sensitive to whether the mode coefficients or their squared values are
considered, whether nonlinear effects are explicitly accounted for, and whether
streamwise and secondary flow structures are separated prior to causality
analyses. We leverage these sensitivities to determine that linear mechanisms
underpin causal relationships between modes that share the same symmetry or
anti-symmetry properties about the corner bisector, while nonlinear effects
govern the causal interactions between symmetric and antisymmetric modes. In
all cases, we find that the secondary flow fluctuations (manifesting as
streamwise vorticial structures) are the primary cause of both the presence and
movement of near-wall streaks towards and away from the duct corners.
