Streamwise oscillations of a cylinder beneath a free surface: Free surface effects on fluid forces

A two-dimensional free surface flow past a circular cylinder forced to performstreamwise oscillations in the presence of an oncoming uniform flow is investigated at a Reynolds number of R = 200 and fixed displacement amplitude, A = 0.13, for the forcing frequency-to-natural shedding frequency ratios, f/f0 = 1.5, 2.5, 3.5. This study is based on numerical solutions of the special integral form of two-dimensional continuity and unsteady Navier-Stokes equations (when a solid body is present) based on a two-fluid model. The method of solution is the same as that employed in [2]. The objective of this study is to examine the effects of the frequency ratio, f/f0, and the cylinder submergence depths, h = 0.25, 0.5, 0.75, on the fluid forces at a fixed Froude number of Fr = 0.2. The link between the changes in the wake dynamics of the cylinder described in [2], and in the properties of fluid forces acting on the cylinder is also discussed. The interaction of waves with moving bodies in the ocean environment is a major source of unsteady loading and vibration on a variety of offshore and coastal structural components including long cables, offshore platforms and risers. The prediction of flow-related unsteady loading on circular cylinders is one of the fundamental steps in hydrodynamic design and control. In this context, the case of a submerged horizontal circular cylinder in a free surface flow has attracted a lot of research efforts which are predominantly experimental. Only few numerical studies have investigated the interaction of a viscous nonlinear free surface wave motion with moving cylindrical bodies (see e.g., [7, 2]). In both of these studies, the free surface effects on the near wake development and vortex formation modes are investigated, but a description of unsteady fluid forces is not given. The present two-dimensional computational study discusses the hydrodynamic forces on a long horizontal cylinder beneath a free surface. The present two-fluid model involve the fluids in the regions Ω1 and Ω2 with densities, ρ1, ρ2, and dynamic