Physics

Reynolds number

Instability

Mathematics

Hele-Shaw flow

Mechanics

Potential flow around a circular cylinder

Turbulence

Cylinder

Geometry

Flow (mathematics)

Wake

Classical mechanics

Flow visualization

Physics of Fluids

Two-dimensional (2D) and three-dimensional (3D) hydrodynamic characteristics of flow past a square cylinder are investigated using direct numerical simulations. The variations of the hydrodynamic forces and wake flow characteristics with the Reynolds number (Re) are examined for Re = 10–400 with a high resolution in Re. Distinct features in the variation trends of the hydrodynamic forces with Re are examined and explained. In addition, for the 3D flows up to Re = 400, three critical conditions are observed at Re of approximately 165.7, 210, and 330. At the onset of the secondary wake instability of Re = 165.7, a sudden increase or decrease in the 3D flow property with respect to its 2D counterpart is observed, which is due to the sudden increase in the flow three-dimensionality at the mode A instability that is subcritical in nature. The second critical condition is because for Re &amp;gt; 210, the mode B flow structure becomes increasingly disordered and the wake flow becomes increasingly turbulent such that the 3D flow property is increasingly deviated from its 2D counterpart. The third critical condition at Re ∼ 330 is related to the disappearance and reappearance of the recirculation regions on the upper and lower sides of the cylinder. While the first two critical conditions are also observed for flow past a circular cylinder, the third one is not since the geometry of a circular cylinder does not give rise to recirculation regions on the upper and lower sides of the cylinder.

Hydrodynamic characteristics of flow past a square cylinder at moderate Reynolds numbers