Vorticity distribution in the flow around a horizontal circular cylinder near a free surface

We perform a numerical study to investigate the flow characteristics around a horizontal circular cylinder near a free surface. The incoming fluid with a uniform velocity (U) flows towards the horizontal cylinder (diameter: D) where the distance between the top position of the cylinder and the still free surface is h. According to the depth ratio (h/D) and the Froude number (U/(gD)^1/2), four kinds of flow patterns are identified; no waves on the free surface, small-amplitude waves on the free surface, surging wave breaking on the free surface with a common vortex shedding behind the cylinder and a jet-like flow on the free surface with a suppressed vortex shedding behind the cylinder. In addition, the free-surface phenomena are all periodic. These numerical findings are compared to experiments and they agree with each other very well. For each experimentally validated numerical case, we check the vorticity distribution both on the free surface and inside the fluid to understand that how the vorticity is conserved.