Leading edge

Wake

Geometry

Boundary layer

Physics

Starting vortex

Reynolds number

Vortex ring

Mathematics

Mechanics

Vortex

Horseshoe vortex

Cylinder

Vortex shedding

Turbulence

Trailing edge

Classical mechanics

Journal of Fluid Mechanics

This study topologically describes near-wall flows around a surface-mounted cylinder at a high Reynolds number ( $Re$ ) of $5\times 10^4$ and in a very thick boundary layer, which were partially measured or technically approximated from the literature. For complete and rational flow construction, we use high-resolution simulations and critical-point theory. The large-scale near-wake vortex is composed of two connected segments rolled up from the sides of the cylinder and from the free end. Another large-scale side vortex clearly roots on two notable foci on the lower side wall. In the junction region, the side vortex moves upwards with a curved trajectory, which induces the formation of nodes on the ground surface. In the free-end region, the side vortex is compressed, which results in a smaller trailing-edge vortex and its downstream movement. Only tip vortices are observed in the far wake. The origin of the tip vortices and their distinction from the near-wake vortex are discussed. Further analyses suggest that $Re$ independence should be treated with high caution when $Re$ increases from 500 to ${O}(10^4)$ . The occurrence of upwash flow behind the cylinder strongly depends on the increase in $Re$ , the mechanism of which is also provided. The separation–reattachment process in the junction region and the trailing-edge vortices are discovered only at a high $Re$ . The former should significantly affect the strength of the side vortex in the junction region and the latter should cause a sharp drop in pressure near the trailing edge.

Topological description of near-wall flows around a surface-mounted square cylinder at high Reynolds numbers