The energy distribution resulting from an impact on a floating body

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 con stant after a short acceleration stage. The present study demonstrates that impact on a floating and non-flared body gives acoustic effects that are l ocalized in time behind the front of the compression wave generated at the moment of impact and are of major significance for explaining the energy di stribution throughout the water, but their contribution to the flow pattern near the body decays with time. We analyse the dependence on the body acce leration 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 impu lse 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 oth er 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 t he body motion during the acceleration stage. The main parameter is the rat io of the time scale for the acoustic effects and the duration of the accel eration 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. Whe n the sphere is impulsively started to a constant velocity (the parameter i s infinitely large), the work takes its maximum value: Longhorn (1952) disc overed that half of this work goes to the kinetic energy of the flow near t he body and the other half is taken away with the compression wave. However , the work required to accelerate the body decreases rapidly as the duratio n of the acceleration stage increases. The optimal acceleration of the sphe re, 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 acce leration. If only the initial velocity of the body is prescribed and it then moves fr eely under the influence of the pressure, the fraction of the energy lost i n acoustic waves depends only on the ratio of the body's mass to the mass o f water displaced by the hemisphere.