Prediction of Parametric Rolling in Irregular Head Waves

  • Hirotada HashimotoEmail author
  • Naoya Umeda
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 119)


For providing a benchmark data for numerical codes for parametric roll prediction, a model experiment of a post-Panamax C11 class containership whose hull form is slightly modified from its original but opened for public was conducted and significant parametric rolling in irregular head waves was recorded. A 3DOF (degrees of freedom) numerical model based on the nonlinear strip theory is developed. The numerical code for time domain simulations is developed for the prediction of large amplitude of parametric roll both in regular and irregular head waves. Comparisons between the model experiment and the numerical simulations show good agreement under the consideration of dispersion due to practical non-ergodicity. By utilizing the developed numerical model, it was demonstrated that small height of the bilge keels is a major reason why significant parametric roll could happen for a C11 class post-Panamax containership in 1998.



Added mass/added moment of inertia

\(b_{1} , b_{2}\)

Linear and quadratic coefficients of roll damping


Wave-making damping coefficient


Diffraction force

\(F_{i}^{FK + B}\)

Froude-Krylov force and buoyancy


Froude number




Wave height


Roll moment of inertia


Pitch moment of inertia


Ship mass




Longitudinal position of centre of gravity


Roll angle


Wave length


Pitch angle


Angular frequency


Heave displacement



This work was supported by a Grant-in Aid for Scientific Research of the Japan Society for Promotion of Science (No. 20760558 & 21360427). The authors express their sincere gratitude to the ITTC (International Towing Tank), as well as MARIN, for providing geometric data of the modified C11 class containership for works on the development of the second generation intact stability criteria. The authors thank also Messrs. Yu Sanya and Yasuhiro Sogawa for their great contribution to this work.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Naval Architecture and Ocean Engineering, Graduate School of EngineeringOsaka UniversitySuita, OsakaJapan

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