Three-dimensional transition in the wake of rectangular cylinders with various aspect ratios: A direct numerical simulation study

This study investigates the three-dimensional (3D) wake transition of flow around rectangular cylinders with seven aspect ratios (AR = 0.25, 0.5, 1, 2, 3, 4, and 5). Direct numerical simulations were performed for Reynolds numbers up to Re = 600. Ten distinct instability modes are observed, manifesting as ordered or disordered states depending on Re and AR. Based on their similarities, these modes are classified into four categories: (i) A, (ii) B, (iii) quasi-periodic, and (iv) quasi-subharmonic. The characteristics of these modes, including their spanwise wavelength and the Reynolds number range in which they emerge, are thoroughly documented for each aspect ratio. The results indicate that increasing the aspect ratio generally raises the critical Reynolds number for the onset of secondary wake transition, with values ranging from approximately Recr = 95 for AR = 0.25 to Recr = 478.5 for AR = 5. However, an earlier onset of three-dimensionality is observed at AR = 4 compared to AR = 3, a phenomenon attributed to variations in vortex shedding dynamics. Furthermore, based on interactions between leading-edge and trailing-edge vortices, three distinct vortex-shedding patterns are identified for elongated cylinders (AR = 3–5). Notably, for the smallest aspect ratio (AR = 0.25), a transition in the base flow from a von Kármán vortex street to a two-layered vortex structure near the cylinder effectively suppresses 3D instabilities, thereby reverting the flow to a two-dimensional state. The study further explores the impact of various instability modes on hydrodynamic forces and vortex shedding frequency.