Flow past a 5:1 rectangular cylinder near a free surface

Rectangular cylinders with an aspect ratio of 5:1 near a free surface are widely used in marine engineering structures, such as immersed tunnels. However, the wake topology and hydrodynamic characteristics, especially the effect of the gap ratio (G=h/D), remain unclear. The improved delayed detached eddy simulation (IDDES) model is used to analyze the flow around a 5:1 rectangular cylinder in proximity to a free surface at Re=1.56×106 and Fr=0.5, considering five gap ratios (G=0.2,0.3,0.5,1.0,1.5). At smaller gap ratios, the confinement from the free surface induces a high-speed, jet-like flow. The deformed free surface functions as a source of surface vorticity, which interacts with the rectangular cylinder wake through a cross-annihilation mechanism, resulting in an asymmetric vortex shedding pattern. As the gap ratio increases, the confinement effect and influence of the jet-like flow correspondingly decrease. Consequently, the reattachment distance of the upper shear layer increases, the wake asymmetry diminishes, and the flow ultimately organizes into a canonical von Kármán vortex street. For small gap ratios, it is easier to agitate the water to produce violent surface distortion compared to high gap ratios. Three distinct surface deformation patterns were identified, and a local Froude number mechanism is used to explain the underlying physics. Notably, a quasi-standing wave is observed on the free surface above the rectangular cylinder when G=1.0 and G=1.5. Dynamic mode decomposition (DMD) confirms that the mean-flow mode dominates the flow energy while vortex-structure modes near the free surface are markedly suppressed at small gap ratios.