Shallow water entry: modeling and experiments

As marine vessels expand their range of operations and their planing speeds increase, understanding the physics of shallow water entry becomes of paramount importance. High-speed impact on the surface is responsible for impulsive hydrodynamic loading, spatiotemporal evolution of which is controlled by the entry speed and the vessel geometry. For shallow water impact, the presence of the ground may further influence the hydrodynamic loading, by constraining the water motion beneath the impacting hull. Here, we present a theoretical and experimental framework to investigate shallow water entry, in the context of the two-dimensional water impact of a wedge. Wagner theory is extended to describe the finiteness of the water column, and the resulting mixed boundary value problem is analytically solved to determine the velocity potential, free surface elevation, and pressure field. To complement and validate the semi-analytical scheme, experiments are performed using particle image velocimetry, by systematically varying the height of the water column. The velocity data are then utilized to reconstruct the pressure field in the fluid and infer the hydrodynamic loading on the wedge. Experimental observations confirm the accuracy of the proposed modeling framework, which is successful in anticipating the role of the bottom wall on the physics of the impact. Our results indicate that the pressure distribution is controlled by the water height, whereby we observe an increase in the pressure at the keel, accompanied by a decrease in the pile-up, as the water column becomes thinner. The results of this study are expected to offer insight into the design of marine vessels and constitute a solid basis for understanding the role of fluid confinement in shallow water entry.