The energy distribution resulting from an impact on a floating body

Abstract

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.