Analysis of autocorrelation function for different wave generation approaches with consideration for Doppler effects

A proper generation of the wave field is fundamental for obtaining reliable results when simulating the dynamics of floating objects in irregular waves. This topic is particularly in focus in the framework of IMO Second Generation Intact Stability Criteria, at direct stability assessment level, where time-domain ship motion simulations are expected to be applied. The generation of the wave field is typically based on the superposition of different harmonic components, with frequencies and amplitudes linked to a discretization of the wave spectrum. The approach used for such discretization affects the characteristics of the generated process and the associated level of correspondence with the original ideal wave elevation process. In this context, the paper considers different approaches that are typically used to generate input waves for ship motion simulations, looking at the autocorrelation function of wave elevation defined in ensemble domain. Analytical results are reported considering the case of zero speed and the case of steady forward speed. Example numerical applications are also provided. In the discussion, attention is given to the possible occurrence of spurious long-time autocorrelations, which can be associated to the occurrence of exact or approximate self-repetitions, as this may impair the quality of simulated ship motions.