Gravity effect on water entry during an early stage

We consider the effects of gravity on the two-dimensional flow caused by a symmetric body vertically entering into initially calm water at constant speed. Surface tension, viscosity and the compressibility of the liquid are neglected. The flow is potential. The region of contact of the water with the body surface starts from a single point and grows monotonically in time. The effects of gravity on the size of the contact region, the hydrodynamic force on the body, the hydrodynamic pressure distribution on the wetted part of the body surface, and the free-surface elevation are analysed for the initial stage of impact, using asymptotic methods with a small-valued gravity-related parameter. It has been well accepted that the effects of gravity on water impact characteristics are small. The analysis reveals that the effects of gravity are relatively small even for impact conditions, where formally these effects should be included in the model. It is found that gravity: slows down the contact points, reduces the hydrodynamic pressure at the periphery of the contact region, but increases the pressure in the central part of the wetted region, and hence increases the total fluid force on the body. The asymptotic contributions are sensitive to the gravity correction to the size of the contact region, even though it is relatively small. The effects of gravity become more important with time for the later stages.