Three-dimensional steep wave impact on a vertical cylinder

In the present study we investigate the 3-D hydrodynamic slamming problem on a vertical cylinder due to the impact of a steep wave that is moving with a steady velocity.The linear theory of the velocity potential is employed by assuming inviscid,incompressible fluid and irrotational flow.As the problem is set in 3-D space,the employment of the Wagner condition is essential.The set of equations we pose,is presented as a mixed boundary value problem for Laplace’s equation in 3-D.Apart from the mixedtype of boundary conditions,the problem is complicated by considering that the region of wetted surface of the cylinder is a set whose boundary depends on the vertical coordinate on the cylinder up to the free-surface.We make some simple assumptions at the start but otherwise we proceed analytically.We find closed-form relations for the hydrodynamic variables,namely the time dependent potential,the pressure impulse,the shape of the wave front(from the contact point to beyond the cylinder) and the slamming force.