Effects of wave-field nonlinearity on motions of ship advancing in irregular waves using HOS method

Abstract

The effects of incident-wave nonlinearity on motions of ships advancing in irregular waves are investigated here in statistical sense. The study is carried out by exploiting the combination of HOS method (High Order Spectral method) and time-domain Rankine source method incorporated with HOBEM (Higher-order Boundary Element Method). In the proposed model, HOS method is employed to simulate nonlinear irregular wave fields in cubic order and Rankine source method incorporated with HOBEM is applied to compute ship wave potential as well as disturbed potential, the equations of motions of ship advancing with constant forward speed in nonlinear waves are further established. Instead of employing simplified steady flow models such as uniform stream, steady ship wave potential is computed beforehand and applied to solve ship motions. Weakly nonlinear scheme considering nonlinear F–K (Froude-Krylov) and restoring forces is adopted.The proposed model is first validated in the case of linear regular and irregular waves via comparisons to experiment data and then applied to three different irregular sea states defined by spectrum with respective BFIs (Benjamin-Feir index). A series of long-time numerical simulations are carried out for both linear wave cases and nonlinear ones, and the statistical properties of nonlinear incident waves and the induced influence on ship motions are investigated and further analyzed. The analysis reveals that with large BFI, the skewness and kurtosis of wave surface elevation manifest departures from Gaussian values and the probability density function (p.d.f.) of the surface elevation performs departures from Gaussian behavior. In nonlinear cases, p.d.f. of instantaneous motions and motion amplitudes as well as exceedance probability of motion amplitudes are notably different from their linear counterparts. Higher possibilities for large motions occur in nonlinear cases.