Hydrodynamic analysis of resonant waves within the gap between a vessel and a vertical quay wall

Concerning the side-by-side offloading operations at gravity-based terminals, the wave interaction with a vessel alongside a long vertical wall in both normal and oblique seas was investigated. The imaging principle was applied to convert the original to an equivalent wave-diffraction problem by two symmetrical vessels in open seas exposed to bi-directional incident waves. The boundary integral equation method, in conjunction with a higher-order boundary element method (HOBEM), was used to solve the equivalent problem. Besides the linear free-surface elevation and wave loads, the second-order mean wave drift loads on the vessel was calculated based on either the direct pressure integration or using a semi-cylindrical control surface. Moreover, the solution was also developed for the oblique wave interaction with a two-dimensional barge-wall system using the eigenfunction expansion matching method. Systemic numerical studies were then conducted for the cases of a rectangular barge and a Wigley hull in close proximity to a long wall, respectively. Under oblique incidence, both the odd and even modes of fluid motion within the gap can be induced. In the case of a rectangular barge, the linear wave force can be obviously amplified at the location of the (1, 0) resonant mode, while the linear wave moment at the (2, 0) mode. In addition, the negative mean force along the transverse direction, which tends to push the barge away from the wall, can be apparently enhanced at both the odd and even resonant modes. Besides, in oblique seas, the (1, 0) resonant mode can give rise to the significant amplification of the positive mean yaw moment around the centre of the cross-sectional area of the barge, which tends to pull the stern of the barge (that faces incident waves) closer to the wall, while pushing the bow away from the wall. Such amplification gets less noticeable for higher modes. Numerical results also indicate that the hull geometry imposes a significant impact on the resonant waves in the gap. In the case of a Wigley hull, the amplification of the free-surface response is much less apparent when compared with a rectangular barge.