Dependence of square cylinder wake on Reynolds number

The wake of a square cylinder is investigated for Reynolds number Re < 107. Two-dimensional (2D) laminar simulation and three-dimensional (3D) large-eddy simulation are conducted at Re ≤ 1.0 × 103, while experiments of hotwire, particle image velocimetry, and force measurements are carried out at a higher Re range of 1.0 × 103 < Re < 4.5 × 104. Furthermore, data covering a wide Re range, from 100 to 107, in the literature are comprehensively collected for discussion and comparison purposes. The dependence on Re of the recirculation bubble size or vortex formation length, wake width, shear-layer transition, time-mean drag force, and Strouhal number is discussed in detail, revealing five flow regimes, each having distinct variations of the above parameters. With increasing Re, while the streamwise recirculation size enlarges at Re < 50 (steady flow regime), the vortex formation length reduces at 50 < Re < 1.6 × 102 (laminar flow regime), remains unchanged at 1.6 × 102 < Re < 2.2 × 102 (2D-to-3D transition flow regime), and decreases at 2.2 × 102 < Re < 1 × 103 (shear layer transition I regime), approaching asymptotically a constant at Re > 1.0 × 103 (shear layer transition II regime). Meanwhile, the wake width decreases with Re in the laminar flow regime, grows in 2D-to-3D transition and shear layer transition I regimes, and levels off in the shear layer transition II regime. The narrowest wake width is identified in the 2D-to-3D transition flow regime, corresponding to a minimum time-mean drag force and a largest Strouhal number. With increasing Re, the shear-layer transition length rapidly declines in the shear layer transition I regime where the transition occurs downstream of the trailing corner of the cylinder. On the other hand, it slowly tapers off in the shear layer transition II regime where the transition takes place upstream of the trailing corner. An extensive comparison is made between the dependence on Re of a circular cylinder wake and a square cylinder wake, with their distinct natures highlighted.