This study presents a numerical investigation for the wavelength effect on the parametric roll in head waves. The computational fluid dynamics (CFD) simulations are carried out for a model-scale ONR Tumblehome to predict the heave, roll, and pitch motions as the parametric roll occurs. An in-house unsteady Reynolds-averaged Navier-Stokes (URANS) solver coupled with a dynamic overset grid approach is applied to the numerical simulations, along with the systematic verification and validation studies based on the experimental data from INSEAN model tests. The parametric roll of the model is then predicted under the regular head waves with different wavelengths, aimed at estimating the instability zone where the parametric roll occurs. The results demonstrate that the parametric roll occurs significantly for the model with Fn = 0.10 as the wavelength is in the range of 0.70-1.20 ship length between perpendiculars (LPP) but it disappears as the wavelength locates outside this range. To analyze the occurrence of the wavelength threshold for the parametric roll zone, the variation of the encounter wave frequency as the ship is advancing in waves is obtained and the relationship between the encounter wave frequency and the parametric roll angle is assessed, which indicate that the variation of the encounter wave frequency induced by different wavelengths is a primary cause leading to the effect on the parametric roll.


Parametric roll is a dangerous roll phenomenon which has been included in the second-generation intact stability criteria proposed by International Maritime Organization (IMO). As a typical dynamic stability failure mode, this phenomenon usually occurs for a ship advancing in head seas, which is related to the periodic time-varying restoring moment of the ship. Owing to the large amplitude induced by the parametric roll, it may cause potential danger for the ship in waves and thereby attracting extensive concerns from many researchers.

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