In this paper, Navier-Stokes simulations around a square cylinder in orbital flow when the flow impulsively starts from rest are performed. The vortex shedding patterns obtained by the simulations are in good agreement with the results of flow visualizations. The computational results demonstrate that the circulation grows during about the first one period, and the circulation strength at stationary state is proportional to the magnitude of incident flow velocity vector. A formula to estimate the inertia coefficient is also deduced considering the lift force due to the circulation.
Flow fields around a vertical cylinder in regular waves or a horizontal cylinder in shallow water regular waves may be idealized as plane oscillatory flow. However, in the case of a horizontal cylinder in deep water regular waves the water particle orbits are almost circular, and an instantaneous incident flow vector rotates with the same sense as the orbital motion during a wave period. At very low Keulegan-Carpenter numbers (Kc), hydrodynamic forces on a bluff body in plane oscillatory flow may safely be predicted by potential flow theory, because there is no large flow separation. However, Chaplin (1984a, 1984b) reported that the inertia force on a horizontal cylinder, with its axis parallel to wave crests, decreases to a value as low as one-half of the inertia force calculated by potential theory at very low Kc numbers (Kc of about 2). He pointed out that the cause of the inertia force reduction is the effect of the lift force, which is always in the opposite direction to the inertia force vector, due to the combination of incident flow and steady circulation generated by the oscillatory boundary layer. Otsuka et al. (1990) carried out flow visualizations and discrete vortex simulations around a horizontal circular cylinder in regular waves.