Study on the coupling effect of water on deck and parametric rolling motion in regular waves

Objectives Both parametric rolling and water on deck are closely related to the stability of ship motion. Studying the interaction between them is a necessary process to evaluate the coupling effect of water on deck and ship nonlinear motion. Methods A three degrees of freedom (3-DOFs) coupling calculation model of ship heave-pitch-parametric rolling considering the effect of shipping water is established within the framework of potential flow theory and numerically solved. Taking the C11 ship as an example, the interaction between parametric rolling and water on deck is studied. Results The research shows that the parametric rolling significantly expands the range of waves with occurrence of shipping water, and increases the overtopping volume and the load generated by the green water. A significant strong nonlinear effect on the righting arm curves in waves is generated by the green water on deck, which reduces the righting arm or even becomes negative. The wave stability of the ship is significantly reduced and the coupling mechanism of water on deck on parametric rolling is revealed. When there is a bulwark on the deck, the shipping water periodically flows into and out of the deck over the bulwark, and there is always a certain amount of water on the deck. The wave overtopping and green water on deck increase the draft of the ship, and there is a certain bow inclination. The amplitude of the parametric rolling response increases, and the above effect increases with the increase of the water accumulation. Conclusions The research results can provide some reference for evaluating the influence of water on deck on the stability of ship.