Vortex shedding and surface waves around a horizontal circular cylinder close to a free surface

Abstract

A fully submerged horizontal circular cylinder close to a free surface moves horizontally below the free surface in a still fluid. Vortex shedding and surface waves are observed according to the relevant Froude number (based on the cylinder diameter) and the gap ratio (distance between the cylinder and the free surface non-dimensionalized by the cylinder diameter). Both constrained and unconstrained cases are considered in terms of the vertical motion of the cylinder due to the vortex shedding. Overall, associated with the vortex shedding, five different surface-wave phenomena are observed

no waves, small-amplitude waves, surging breaking waves, collapsing breaking waves (observed only in unconstrained cases), straight-streamline jet-like flows over the upper surface of the cylinder. In the case of no wave motion and small amplitude wave, Karman vortex is formed. However, in the surging wave, a new vortex layer is formed when the free surface is broken due to abrupt deformation of the free surface. This vortex layer affects the vortex shedding behind a cylinder, so that the oscillating amplitude of the cylinder is not constant. When the vibration of the cylinder become significantly larger, a collapsing wave is formed and the oscillating amplitude of the cylinder is kept constant. Jet-like flow is a diagonal flow formed at a close distance from the free surface to the cylinder surface, suppressing vortex shedding and reducing cylinder vibration. In particular, for a constant gap ratio, the jet-like flow becomes steeper as the Froude number increases and, for a constant Froude number, the jet-like flow becomes steeper as the gap ratio decreases. In the presence of a free surface, there have been few studies involving both constrained cylinders and unconstrained cylinders. Therefore, the results of this study are expected to help to analyze the hydrodynamic characteristics that occur when an underwater structure is placed close to a free surface.