Higher-order harmonic induced wave resonance for two side-by-side boxes in close proximity

Wave resonance in a narrow gap formed by two boxes in the side-by-side arrangement is investigated by employing a numerical wave flume based on the OpenFOAM® package. In the present study, the main focus lies in the exploration of the nonlinear resonant behavior induced by the second- and third-order harmonic components which occur around half and one third of the resonant frequencies. A wide range of incident wave frequencies is considered, by which the higher-order harmonic induced wave resonance at lower wave frequencies is discussed. By the harmonic analysis, it is revealed that at the resonant frequency the first-order harmonic component dominates the wave resonance and the second-order effect is minor, which coincides with the conclusion drawn in the previous study. However, around half or one third of the resonant frequencies, the first-order harmonic component is in good agreement with the linear potential flow solutions, but the second- or third-order harmonic component is significant, causing the corresponding higher-order harmonic induced wave resonance. In addition, the numerical results show that the second- and third-order harmonic induced wave resonances only influence the wave properties inside the narrow gap, such as the wave response in the narrow gap and the horizontal wave forces on the boxes. The wave responses around the two-box system, the vertical wave forces on the boxes and the reflection and transmission coefficients are hardly affected by the wave resonance around the corresponding half and one third of the resonant frequencies. The higher-order harmonic induced normalized wave elevation in the narrow gap increases with the increase in incident wave height, implying the increased influence of the free surface nonlinearity.