  We carry out Direct Numerical Simulation (DNS) of flows in closed rectangular
ducts with several aspect ratios. The Navier-Stokes equations are discretized
through a second-order finite difference scheme, with non-uniform grids in two
directions. The duct cross-sectional area is maintained constant as well as the
flow rate, which allows to investigate which is the appropriate length scale in
the Reynolds number for a good scaling in the laminar and in the fully
turbulent regimes. We find that the Reynolds number based on the half length of
the short side leads to a critical Reynolds number which is independent on the
aspect ratio (AR), for ducts with AR>1. The mean and rms wall-normal velocity
profiles are found to scale with the local value of the friction velocity. At
high friction Reynolds numbers, the Reynolds number dependence is similar to
that in turbulent plane channels, hence flows in rectangular ducts allow to
investigate the Reynolds number dependency through a reduced number of
simulations. At low Re the profiles of the statistics differ from those in the
two-dimensional channel due to the interaction of flow structures of different
size. The projection of the velocity vector and of the Reynolds stress tensor
along the eigenvectors of the strain-rate tensor yields reduced Reynolds stress
anisotropy, and simple turbulent kinetic energy budgets.
