Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Numerical Study on Inner Mechanism of Ship Parametric Roll in Head Waves
Huawei ZHOU a,i, Lufeng Pan a, Ximin Tian a, Ping Xu a, Renchuan ZHUba

Marine Design & Research Institute of China, Shanghai, ChinabShanghai Jiao Tong University, Shanghai, China

ABSTRACTwith a semi-empirical formula for surge motion to predict theparametric roll of a ship. Chu, Wu and Lu et al. (2016) constructed atime-domain hybrid model with free surface green function in innerdomain and Rankine source in outer domain to simulate the parametricroll considering the couplings among heave, roll and pitch modes. Liuand Papanikolaou (2016) constructed a 3D time-domain model based on
the IRF concept and zero-speed free surface green function to predictthe parametric roll in waves. Kim and Kim (2011) compared different
numerical methods and concluded that the results from the direct
time-domain method and the IRF method agree well.

Ship parametric roll is one of the stability failure modes of thesecond-generation intact stability criteria developed by the InternationalMaritime Organization (IMO) recently. In this paper, a 6-DOF
three-dimensional weakly nonlinear time-domain model based on theIRF (Impulse Response Function) method is constructed to predict ship
parametric roll in head waves. It is verified by the experimental resultsof C11 containership. On this basis, the inner mechanism of parametricroll is revealed by investigating the time-history and resonancefrequencies of restoring forces and coefficients numerically.
Additionally, the influence of ship speed and wave height on parametricroll occurrence and amplitude is further investigated.

In the IRF method, lots of theories were employed to solve thefrequency-domain problem and obtain hydrodynamic coefficients at full
frequency range, such as strip theory (Salvesen, 1970), zero-speed greenfunction method combined with speed correction (Newman, 1985),
non-zero speed green function method (Hong et al. 2016), Rankine
source (Bruzzone et al. 2011), and so on. The non-zero speed Havelock
form translating-pulsating source green function method has been
proven to have an acceptable balance between accuracy and computing
efficient (Hong et al. 2016).

KEY WORDS: Parametric roll; impulse response function;
time-domain model; numerical study; inner mechanism.

INTRODUCTION
Ship parametric roll is considered to be one of the five stability failuremodes and is introduced into the second-generation intact stability
criteria by the IMO recently due to its incidence rate and huge hazard,
such as the accident of a C11 class post Panamax containership (France,et al. 2003).The main mechanism of parametric roll has been
acknowledged by scientists in earlier times (Watanabe, 1934).
Essentially, it’s a parametric resonance phenomenon due to the periodic
change of the metacentric height and characterized by large-amplitude
ship roll in head waves. Such as containership, Ro-Ro ship and fishingship usually have a bow with large flare and a flat stern together, which
may cause great changes of water plane in waves and lead to periodic
stability changes. When the period meets the parametric resonanceperiod, large-amplitude roll motion can be triggered.

In this paper, a 6-DOF time-domain model based on the IRF concept
and the non-zero speed Havelock form translating-pulsating source
green function method is constructed to predict the parametric roll. The
Froude-Krylov forces and the restoring forces are calculated on theinstantaneous wet surface while the radiation and diffraction forces are
kept linear by transforming from frequency-domain results. The model
is applied to simulate the parametric roll resonance of C11
containership in head waves and compared with experiment. Based on
the good agreement between the simulation and experiment, the innermechanism and major factors of the ship parametric roll are investigatednumerically.

THEORY of IRF METHOD for SHIP MOTIONS in
TIME-DOMAIN

Various numerical methods in potential theory framework have been
applied to simulate the parametric roll in time-domain, which can bedivided into direct time-domain method and the IRF method in
accordance with procedures to obtain radiation and diffraction forces.
Both concentrate on simulating nonlinear restoring forces and incidentwave forces while keep the diffraction and radiation forces linear toobtain the balance between accuracy and time. Silva and Soares (2013)
constructed a time-domain strip theory model and a 6-DOF procedure

The right-hand coordinate system OXYZ is fixed on the plane ofundisturbed water surface and advancing forward with the ship speed
U0 . The origin is located at the middle of the ship, with x-axis pointing
to the bow, and y-axis pointing to the port.

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