On the spatiotemporal dynamics of multi-mode fluid resonance in moonpools with recess

Wave-induced nonlinear fluid resonance in moonpools with a recess is numerically investigated in this work based on a two-dimensional multiphase viscous flow solver. The objective is to explore the spatiotemporal dynamics of wave resonance, with a particular emphasis on identifying modal contributions, characterizing nonlinear harmonic interactions, and revealing frequency-dependent mode transitions. This study aims to provide new insight into the fundamental mechanisms governing multi-modal fluid resonance under nonlinear and viscous conditions. Two distinct temporal evolution regimes of resonant fluid oscillations, i.e., piston-mode and sloshing-mode resonance, are clarified via time-resolved wavelet spectra and phase dynamics analysis. The piston mode exhibits linear, coherent oscillations characterized by phase locking state, whereas the sloshing mode demonstrates strong nonlinearity, higher-order harmonic generation, and nonlinear phase trapping behavior. A mode displacement superposition mathematical approach is employed to quantify the modal contributions, revealing frequency-dependent energy exchange between piston and sloshing modes, particularly near superharmonic resonance conditions. Spatial analysis further shows that resonant amplification is highly localized, with certain modal responses absent at nodal positions. Harmonic decomposition confirms the critical role of nonlinear energy redistribution at or around the superharmonic resonant frequencies. The physical insight gained from this study advances the understanding of the dynamic establishment of the complex multi-mode moonpool resonance and offers valuable guidance for future modal analysis.