A Two-Dimensional Weibull Distribution and Its Application to Rolling

Abstract

A two-dimensional Weibull distribution is presented which is obtained by transforming a two-dimensional Rayleigh distribution. The emphasis herein is on its application to describe the statistics of successive wave periods, and the results are illustrated by discussing the rolling of smaller vessels in beam seas in a simplified manner. Reference is also made to the related subjects on the joint correlation of successive high waves and on the joint statistics of wave steepness parameters for two successive waves, where the wave steepness parameters considered are the crest front steepness and the total wave steepness.