Radiation hydrodynamics of floating vertical cylinder in viscous fluid

Fully nonlinear axisymmetric viscous flow due to heave oscillation of a surface-piercing vertical cylinder is analyzed using a finite-difference method based on curvilinear coordinates. Of significance to numerical modeling is the present finding that the free-slip condition used to model the movement of the contact line affects neither the overall flow nor the hydrodynamic pressure force acting on vertical cylinder. The viscous-flow results are compared with fully nonlinear inviscid-flow results, which are obtained using a mixed Eulerian-Lagrangian formulation, to contrast the effects of viscosity on the flow field, hydrodynamic force, and radiating surface waves. New results are presented for a range of parameters to illustrate physical mechanisms of the inception and evolution of vertical structures due to body motion in a free surface and their effects on the hydrodynamic force.