Design waves and statistics of linear gap resonances in random seas

Water wave resonance between two side-by-side vessels is a multimode resonant hydrodynamic phenomenon with low damping. The potential flow damping and viscous damping inside the gap play a significant role, influencing the amplitudes of the gap resonances. The frequencies of the gap modes can be well predicted by linear potential flow theory, while much effort has been made to explore the nature of viscous damping. A series of experiments are conducted to explore the temporal (Zhao et al., Journal of Fluid Mechanics, vol. 812, 2017, 905–939) and spatial structure (Zhao et al., Journal of Fluid Mechanics, vol. 883, 2020, A22) of the resonant responses along the gap. Ultimately, it is of practical interest to understand the response statistics along the gap in random seas, to facilitate decision-making for safe offshore operations. Following our previous studies which focused on new physics, here identify the design waves that produce the most probable maximum responses under unidirectional random linear wave excitation. This is achieved through an efficient prediction model within a linear theory. Combining the experimental data and linear potential flow calculations, we provide the lower and upper bounds of gap responses, bracketing possible responses at the field scale. The statistical model is expected to be of practical importance for offshore operations.