  In this stub article, we show that laminar quasi-periodically developed flow
is characterized by velocity and pressure modes which decay exponentially along
the main flow direction. As the amplitudes of these modes exhibit streamwise
periodicity, they can be determined on a single transversal row of the array.
Their shape and corresponding decay rate are governed by an eigenvalue problem
which generalizes the Orr-Sommerfeld equation for quasi-developed Poiseuille
flow. By means of full-scale channel flow simulations, we numerically
investigate the onset point, extent, eigenvalues and perturbation sizes of
quasi-periodically developed flow in channels with equidistant in-line square
cylinders, assuming a parabolic inlet velocity profile. In particular, the
dependence on the mass flow rate, the aspect ratio and height of the channel is
discussed, considering three porosities of the cylinder array (0.75, 0.89 and
0.94), and Reynolds numbers from 20 to 300, based on a reference length of
twice the channel height. It is observed that the region of quasi-periodically
developed flow covers a large part of the region of flow development in the
channel. Therefore, the corresponding eigenvalues explain largely the observed
scaling laws for the onset point of periodically developed flow.
