Transient design waves for green-water loading on bulk carriers

The wave surface profiles associated with extreme relative motion between a slender stationary vessel and the adjacent wave surface are investigated for long-crested head seas. The methodology is based upon an established statistical relationship for a Gaussian random process which indicates that in the vicinity of an extreme event the most probable shape of the time history approaches that of the autocorrelation function. Attention is given to the relative motion at a longitudinal position which is representative of the No. 1 hatch cover location on a bulk carrier. Second-order corrections to the wave surface profiles are used to provide estimates of nonlinear relative motions. It is shown that extreme relative motion at the hatch cover location is associated with the vessel encountering a steep-fronted wave with pronounced asymmetry in the horizontal and vertical directions. In order to evaluate the exceedence probabilities, it is hypothesized that the peaks of the nonlinear relative motions are closely correlated with the peaks of an underlying linear process. The overall methodology is applied to an investigation of relative motion exceedence probabilities for vessel lengths of 250 m and 300 m over a range of survival sea states.