  There is an increasing need to develop a two-dimensional (2D) water entry
model including the slamming and transition stages for the 2.5-dimensional
(2.5D) method being used on the take-off and water landing of seaplanes, and
for the strip theory or 2D+t theory being used on the hull slamming. Motivated
by that, this paper numerically studies the transition stage of the water entry
of a linear wedge with constant and varying speeds, with assumptions that the
fluid is incompressible, inviscid and with negligible effects of gravity and
surface tension, and the flow is irrotational. For the constant speed impact,
the similitude of the declining forces of different deadrise angles in the
transition stage are found by scaling the difference between the maximum values
in the slamming stage and the results of steady supercavitating flow. The
formulation of the hydrodynamic force is conducted based on the similitude of
the declining forces in the transition stage together with the linear
increasing results in the slamming stage. For the varying speed impact, the
hydrodynamic force caused by the acceleration effect in the transition stage is
formulated by an added mass coefficient with an averaged increase of 27.13%
compared with that of slamming stage. Finally, a general expression of the
hydrodynamic forces in both the slamming and transition stages is thus proposed
and has good predictions in the ranges of deadrise angles from 5 deg to 70 deg
for both the constant and varying speed impacts.
