  The aim of this work is to analyse the formation mechanisms of large-scale
coherent structures in the flow around a wall-mounted square cylinder, due to
their impact on pollutant transport within cities. To this end, we assess
causal relations between the modes of a reduced-order model obtained by
applying proper-orthogonal decomposition to high-fidelity-simulation data of
the flow case under study. The causal relations are identified using
conditional transfer entropy, which is an information-theoretical quantity that
estimates the amount of information contained in the past of one variable about
another. This allows for an understanding of the origins and evolution of
different phenomena in the flow, with the aim of identifying the modes
responsible for the formation of the main vortical structures. Our approach
unveils that vortex-breaker modes are the most causal modes, in particular,
over higher-order modes, and no significant causal relationships were found for
vortex-generator modes. We validate this technique by determining the causal
relations present in the nine-equation model of near-wall turbulence developed
by Moehlis et al. (New J. Phys, vol. 6, 2004, p. 56), which are in good
agreement with literature results for turbulent channel flows.
