The initial stage of the water flow caused by an impact on a floating body is
considered. The vertical velocity of the body is prescribed and kept constant after a
short acceleration stage. The present study demonstrates that impact on a floating and
non-flared body gives acoustic effects that are localized in time behind the front of the
compression wave generated at the moment of impact and are of major significance
for explaining the energy distribution throughout the water, but their contribution to
the flow pattern near the body decays with time. We analyse the dependence on the
body acceleration of both the water flow and the energy distribution – temporal and
spatial. Calculations are performed for a half-submerged sphere within the framework
of the acoustic approximation. It is shown that the pressure impulse and the total
impulse of the flow are independent of the history of the body motion and are readily
found from pressure-impulse theory. On the other hand, the work done to oppose the
pressure force, the internal energy of the water and its kinetic energy are essentially
dependent on details of the body motion during the acceleration stage. The main
parameter is the ratio of the time scale for the acoustic effects and the duration of the
acceleration stage. When this parameter is small the work done to accelerate the body
is minimal and is spent mostly on the kinetic energy of the flow. When the sphere is
impulsively started to a constant velocity (the parameter is infinitely large), the work
takes its maximum value: Longhorn (1952) discovered that half of this work goes to
the kinetic energy of the flow near the body and the other half is taken away with
the compression wave. However, the work required to accelerate the body decreases
rapidly as the duration of the acceleration stage increases. The optimal acceleration
of the sphere, which minimizes the acoustic energy, is determined for a given duration
of the acceleration stage. Roughly speaking, the optimal acceleration is a combination
of both sudden changes of the sphere velocity and uniform acceleration.If only the initial velocity of the body is prescribed and it then moves freely under
the influence of the pressure, the fraction of the energy lost in acoustic waves depends
only on the ratio of the body's mass to the mass of water displaced by the hemisphere.
Prediction for Irregular Ocean Wave and Floating Body Motion by Regularization: Part 2. Motion Prediction