Three-Dimensional Sloshing of Water on Decks

A methodology is proposed to solve the problem of the three-dimensional flow of water sloshing on the deck of a vessel, and to calculate the resulting forces and moments at the center of gravity. The Eulerian equations of motion of the water particle for incompressible inviscid shallow water flow are formulated with respect to a system attached to the oscillating vessel. The system of the nonlinear hyperbolic equations of motion is solved numerically using Glimm's method (random-choice method). Complex flow patterns consisting of oblique bores and "swirling" motions of the water on deck were revealed, for a vessel oscillating in roll and pitch motions, for a wide range of excitation frequencies. Large accumulation of water occurs at the corners while parts of the deck become dry. Significant rolling moments due to sloshing are exerted on the vessel. These must be taken into account when the dynamic response of the vessel is studied.