Nonlinear Roll Motion of a Flooded Ship in Regular Waves

Abstract

This paper describes dynamic effects of flooded water on nonlinear roll motion of a ship in regular beam waves. Experiments using a ferry model demonstrate nonlinear roll response of a flooded ship in waves. It is found that two kinds of roll motion with different amplitudes and periods coexist and that one of them is particularly irregular and complicated even in regular waves of relatively moderate amplitude. The reconstructed attractor of the roll motion in a delay-coordinate state space shows that it is not simple harmonic motion. In order to further study this complicated roll motion, we derived model equations which include both the nonlinear effects of the restoring moment and the coupling effects of roll and flooded water. The dynamic motion of flooded water produces the coupling effects which have been neglected in most previous works. Numerical solutions of the model equations show that this coupled system yields nonlinear phenomena similar to the experimental results. In addition, we also experimentally studied motion of a box-shaped model with flooded water in regular waves. The experimental results show that the roll response varies with changing the wave height in a complicated manner which also depends on the amount of flooded water, and that some of complicated roll motion have typical properties of low-dimensional deterministic chaos. These results suggest that the nonlinearly coupled dynamics of a ship and flooded water is a key to solve this problem.