The transient responses in the fixed and free-heaving moonpools under the conditions of linear and nonlinear gap resonance are investigated. A two-dimensional numerical model was established using a constrained interpolation profile method-based in-house code. This paper mainly concentrates on the prediction and quantification of the developing and diminishing processes of the free-surface elevation at gap when encountering both the linear gap resonance and quadratic wave excitation (QWE)-driven gap resonance. The parameter analyses with respect to the distance between the barges and barge draft are considered to derive the variation in the response time and damping time. The continuous wavelet transform (CWT) is introduced to investigate the gap resonances for the first time to obtain the transient characteristics' distribution of the free-surface elevation at gap along time and frequency domains. Numerical results demonstrate that the heave motion has changed the developing patterns of both the linear gap resonance and QWE gap resonance in the free-heaving moonpool rather than those in the fixed moonpool. Nevertheless, the impact caused by heave is little as for the diminishment. By introducing a new hyperbolic-function-type amplification function, the development of the gap resonances for the free-heaving moonpool is well predicted. In addition, the opposite tendency is observed for both the response time and damping time between the fixed and free-heaving moonpools when considering from the linear to QWE gap resonances. According to the transient characteristics obtained from the CWT, it is attributed to the different proportions of the free-surface elevation's second-order component between the fixed and free-heaving moonpools at the QWE resonant point. Moreover, the duration of the damping time is found to be greatly influenced by the phase relation between the free-surface elevation at gap and the heave motion of the moonpool from the linear resonant point to the QWE resonant point.

The hydrodynamic characteristics of the gap resonances between two identical side-by-side barges are investigated in a constrained interpolation profile method-based numerical wave tank. Each barge can heave freely under the excitation of the incident waves. This paper mainly concentrates on the influences of the nonlinearities during the gap resonances on their hydrodynamic performance, via the parameter study of the incident-wave height. Numerical results demonstrated that the nonlinear gap resonances' magnitudes may reach close to or exceed that of the linear gap resonance and naturally contain strong nonlinearities when considering the heave responses of the side-by-side barges. Meanwhile, the effects of the heave responses on the key hydrodynamic parameters cannot be ignored as well. Therefore, the wave run-ups of the barges are of significant importance for the investigation. On the one hand, the wave run-ups directly reflect the coupling effects between the gap resonances and the twin barges' heave responses. On the other hand, the nonlinearities of the wave run-ups perform stronger than the wave elevation at the gap. Moreover, the linear wave run-ups are proposed via the linear formulas to qualitatively and quantitively investigate the effects of the nonlinearities on the inner process of the wave run-ups by comparison. Based on the harmonic analysis, the features of the distributions of the first four order harmonics of the wave elevation at the gap, the wave run-ups, and the wave loads are illustrated.

The linear and nonlinear gap resonances in a free-rolling moonpool are investigated using a two-dimensional in-house code based on the constrained interpolation profile method. This study primarily focuses on the effects of roll motion on hydrodynamic characteristics, taking into account both the linear gap resonance and the nonlinear process-driven gap resonances. The analysis of the incident-wave height is conducted to illustrate the relationship between higher-order harmonics and nonlinear gap resonances. Numerical results demonstrate that the resonant frequency is insensitive to the roll motion. However, the roll response plays an important role in influencing the vertical wave loads on the barges and affecting the energy conversion pattern in the fluid field. According to the analysis of the incident-wave height parameter, the magnitudes of resonance at the linear and nonlinear resonant points are approximately in sub-linear and superlinear relationships with the incident-wave height, respectively. Moreover, the vortex shedding modes around the entrance of the free-rolling moonpool gradually transit from being dominated by the pairs of vortices to being dominated by the single vortex as the gap resonance changes from linear to quartic.

The hydrodynamic characteristics of a free-floating moonpool encountering the gap resonances are investigated based on the constrained interpolation profile method in numerical wave tank. This paper mainly concentrates on the influences of the moonpool's motion responses and the incident-wave height on the gap resonances in the free-floating moonpool. Numerical results demonstrated that the heave response significantly changes the frequency and the magnitude of the linear gap resonance, while the roll motion influences more on the vertical wave loads and the wave responses in the fluid field. The heave and roll response of the free-floating moonpool are generally independent. Moreover, the magnitudes of the nonlinear gap resonances have the tendency of catching up and exceeding the linear gap resonance as the incident-wave height increasing for the free-floating moonpool, which is the consequence of the higher-order harmonics driven by the nonlinear processes and the linear secondary resonant region induced by the heave response. Based on the wavelet transform, it could be observed that the amplified harmonic component usually takes more time to be fully developed than other harmonic components during the development of its corresponding nonlinear gap resonance.