Hydrodynamic impact of an elliptic paraboloid on cylindrical waves

The linearized Wagner theory is used to describe the initial stage of the penetration of an elliptic paraboloid on the crest of a regular wave. It is shown that the asymptotic solution for small wave steepness and large enough radii of curvature of the body is obtained from a slight modification of the standard impact problem without a wave. In practice the boundary value problem is formulated for a fictitious elliptic paraboloid: its radii of curvature are modified compared to the actual ones and its kinematics of penetration makes mainly a horizontal velocity appear due to the velocity of the propagating crest. To validate the present approach, an experimental campaign is carried out. The combined choice of the wave parameters and the geometric characteristics of the body leads to a circular expanding wetted surface. The experimental data confirm the theoretical results. Comparisons made for the pressure and the force show a satisfactory agreement.