Computational fluid dynamics-based study on parametric roll behavior of a container ship in cross waves

Parametric roll is a critical nonlinear phenomenon that may induce large amplitude roll motions and pose significant risks to the safety of ships, especially when triggered by longitudinal waves. However, parametric roll in cross wave conditions remains insufficiently investigated. This study investigates the parametric roll behavior of a C11 class container ship encountering cross waves in head seas, using computational fluid dynamics simulations. A numerical wave tank is established based on the computational fluid dynamics software STAR-CCM+, and the ship's dynamic motion responses are simulated. A systematic sensitivity analysis of ship parametric roll with respect to cross wave amplitude, wavelength, ship forward speed, and wave encounter frequency is conducted, using a controlled variable approach to ensure the independent assessment of each factor. Furthermore, the influence of water depth on the parametric roll behavior is explored. The results indicate that, under identical wave conditions, cross waves induce significantly more intense parametric roll motion than regular unidirectional waves. Under varying water depths and speeds, when the cross wave amplitude reaches a certain threshold and the wave encounter frequency approaches approximately twice the natural roll frequency of the ship, the parametric roll becomes most pronounced, with roll amplitudes increasing progressively with wave height. When the incident wavelength is comparable to the ship length, the periodic variation of the restoring moment becomes most prominent, which tends to trigger a sharp increase in roll amplitude. Since the wave encounter frequency is determined by both wave frequency and ship speed, adjusting the ship speed and direction provides an effective strategy to suppress the occurrence of parametric roll.