Dependence of Roll and Roll Rate in Nonlinear Ship Motions in Following and Stern Quartering Seas

Abstract

The changing stability of a ship in waves may have a significant influence on the probabilistic properties of roll in irregular following and quartering seas. In particular, nonlinear effects may lead to dependence between roll angles and rates, which will have significant repercussions on the application of the theory of upcrossings for evaluating the probability of a stability failure related to roll motion such as capsizing. The roll response of a ship in a stationary seaway is a stationary stochastic process. For such a process, the roll angle and its first derivative are, by definition, not correlated and are often assumed to be independent. However, this independence can only be assumed a priori for normal processes, and the nonlinearity of large-amplitude roll motions can lead to a deviation from normal distribution. In the present work, the independence of roll angles and rates is studied from the results of numerical simulations from the Large Amplitude Motion Program (LAMP), which includes a general body-nonlinear calculation of the Froude-Krylov and hydrostatic restoring forces. These simulations show that, for the considered case, roll and roll rate are independent in beam seas, even though the distribution of the roll response is not normal. However, roll angles and roll rates for stern quartering seas are not independent.