  The wake topology developing behind a wall-mounted square cylinder in a
turbulent boundary layer has been investigated using a high-resolution
large-eddy simulation (LES). The boundary-layer thickness at the obstacle
location is fixed, the Reynolds number based on the cylinder h and the incoming
free-stream velocity $u_\infty$ is 10,000 while the aspect ratio (AR), defined
as obstacle height divided by its width, ranges from 1 to 4. The Reynolds
stresses, anisotropy-invariant maps (AIM) and the turbulent kinetic energy
(TKE) budget are analyzed to investigate the influence of AR on the wake
structures and on the turbulence production and transport. In particular, the
transition from a dipole configuration for low AR to a quadrupole wake is
extensively discussed and examined. The necessity of more data to express this
critical AR as a function of the momentum-thickness-based Reynolds number
$Re_{\theta}$ is thus highlighted. As an effect of the AR, the wake is deformed
in both streamwise and spanwise directions. This contraction of the wake,
attributed to the occurrence of the base vortices for the cases AR = 3 and 4,
impacts the size of the positive production region that stretches from the roof
and the flank of the obstacle to the wake core. The AIMs confirm the wake
three-dimensionality and are used to describe the redistribution of the
turbulent kinetic energy (TKE) along the three normal directions, in agreement
with the literature [A. J. Simonsen and P. Krogstad, Phys. Fluids 17, 088103,
(2005)]. The present analysis on the TKE budget displays a stronger turbulence
production for the cases AR = 3 and 4, demonstrating the strong influence of
the tip and base vortices in generating turbulence at the wall location behind
the cylinder.
