The wake topology behind a wall-mounted square cylinder immersed in a turbulent boundary layer is investigated using high-resolution large-eddy simulations (LES). The boundary-layer thickness at the obstacle location is fixed, with a Reynolds number based on cylinder height ℎ and free-stream velocity 𝑢∞ of 10,000 while the aspect ratio (AR), defined as obstacle height divided by its width, ranges from 1 to 4. The mesh resolution is comparable to DNS standards used for similar wall-mounted obstacles, though with relatively lower Reynolds numbers. The effects of AR on wake structures, turbulence production, and transport are analyzed via Reynolds stresses, anisotropy-invariant maps (AIM), and the turbulent kinetic energy (TKE)budget. In particular, the transition from ‘‘dipole’’ to a ‘‘quadrupole’’ wake is extensively examined as AR increases. With increasing AR, the wake shrinks in both the streamwise and spanwise directions, attributed to the occurrence of the base vortices (AR = 3 and 4). This change in the flow structure also affects the size of the positive-production region that extends from the roof and the flank of the obstacle to the wake core. The AIMs confirm three-dimensional wake features, showing TKE redistribution in all directions (Simonsen and Krogstad, 2005). Stronger turbulence production in AR = 3 and 4 cases highlights the role of tip and base vortices behind the cylinder. The overall aim is to refine the dipole-to-quadrupole transition as a function of AR and accounting for the incoming TBL properties. The novelty relies on proposing the momentum-thickness-based Reynolds number Re𝜃 as a discriminant for assessing TBL effects on turbulent wake structures.