The effect of a recess on the nonlinear free-surface responses of three-dimensional moonpools

The nonlinear free-surface response of moonpools with recesses is investigated through both experimental and theoretical analyses. A theoretical model is developed to compute the natural frequencies using linearised potential flow theory and eigenfunction expansions. Four moonpool configurations with varying recess lengths are examined experimentally. The analysis reveals that larger recess lengths correspond to increasingly pronounced nonlinear responses. It is also shown that, for an incident wave group with suitable frequency content, the linear moonpool response can be significantly smaller than the second- and third-harmonic components. This effect is attributed to super-harmonic secondary resonance, characterised by $n \omega =\omega _{pq}$ ( $n\geqslant 2$ and $p+q\geqslant 1$ ), where $n$ denotes the super-harmonic order, $\omega$ is the excitation frequency, and $p$ and $q$ are the longitudinal and transverse mode numbers, respectively. Here, $\omega_{pq}$ represents the sloshing frequency of the three-dimensional moonpool. Furthermore, it is found that, as the primary responses increase, cross-flow instability can lead to secondary resonance in non-symmetric modes. This occurs because the double and triple frequencies of the base mode approach the transverse or diagonal sloshing frequencies. Additionally, hard-spring Duffing effects for secondary resonance induced by super-harmonics are observed in cases with recesses, becoming more pronounced as the recess length increases, particularly when $h/l\lt 0.3368$ , where $h$ is the water depth above the recess and $l$ is the moonpool length.