Numerical Study on Difference-Frequency-Induced Parametric Roll Occurrence

Abstract

This study considers the parametric roll phenomena of large container and cruise ships. In particular, a new mechanism of the occurrence of parametric roll is introduced in this paper. This new mechanism is due to the difference-frequency effects in the presence of bichromatic waves. To prove the present finding, theoretical, numerical and experimental methods are applied. In the numerical approach, nonlinear roll motion is simulated by using 2 different time-domain methods: the impulse-response-function method and the 3D Rankine panel method; in particular, a weakly nonlinear method including nonlinear Froude-Krylov and restoring forces is applied. These 2 methods provide favorable results for parametric roll occurrence. The unstable parametric roll is theoretically examined by introducing the quasi-periodic Mathieu equation. Unstable criteria are well predicted from stability analysis in the theoretical approach. The occurrence is also observed in the experiment carried out in an ocean basin.