On the nonlinear modeling of parametric rolling in regular and irregular waves

This paper summarizes the results and the problems still open regarding the development of a 1.5DOF nonlinear mathematical model of the parametric rolling in longitudinal waves with particular regard to the head sea condition. A first part is devoted to the case of regular waves, while the second concerns parametric rolling generated by irregular waves obtained by means of white noise filtered through a linear filter with adjustable bandwidth and by using a Bretschneider spectrum. The availability of an extensive series of test results on scale models conducted at University of Trieste and at INSEAN, allows a thorough discussion of the problems connected with the threshold formulation for parametric rolling and its amplitude modelling above threshold.