Nonhnear axisymmetric viscous and inviscid solutions corresponding to heave oscillation of a submerged vertical cylinder are presented in this paper. The fully nonlinear free-surface flow problem is solved using finite-difference method based on curvilinear coordinates. A primitive-variables based fractional-step formulation is used for the analysis of viscous flow, while a mixed Eulerian-Lagrangian formulation for that of inviscid flow. New results obtained for a range of amplitudes and frequencies of body oscillation and mean depth of body submergence, demonstrate effects of free surface on the dynamics of body-generated vortices and on the vortical component of hydrodynamic force acting on the body. For example, a rapid radial transport of body-generated vortex rings, accompanied by breaking of a short wave by local instability, is observed in the case of shallow submergence and low frequency of oscillation. At intermediate frequency, interaction between vortical and wave motions results in the formation of a dipole-type pair of vortex rings. Comparison of viscous and inviscid solutions show that the vortex structures could significantly modify the near-field wave signature and also affect hydrodynamic force acting on the body. Present results of three-dimensional heave motion also reveal the occurrence of negative added mass at intermediate frequency when the submergence of the cylinder is small. Force calculations reaffirm that effect of viscosity on hydrodynamic forces is of significance at low and intermediate frequencies of body oscillation.
Study of near-surface wave-body interactions is of significance in many ocean engineering and naval architecture applications. Prediction of motion response of ocean vehicles to surface waves, determination of wave loads on offshore structures, design of buoy systems for oceanographic measurements are examples of such applications. From a scientific viewpoint, the study is of importance for understanding vorticity generation, vortex dynamics, and flow turbulence in the presence of a free surface.
