Two-dimensional numerical study on the effect of water depth on resonance behaviour of the fluid trapped between two side-by-side bodies

• Effect of water depth on gap resonance of two bodies is examined numerically.
• Resonant frequencies and wave heights depend apparently on water depth.
• Water depth effect is negligible if its ratio to body draft is larger than six.
• Potential flow fails to predict the trend of resonance height with water depth.

The effect of water depth on gap resonance of two side-by-side rectangular boxes is examined in a 2D numerical wave flume at various gap widths and body drafts. The numerical model used is based on the volume of fluid (VOF) method for the solution of Navier–Stokes equations combined with free surfaces. The water depth covered ranges from shallow to deep water regimes. It is found that the resonant frequencies and wave heights depend apparently on water depth. For a given body draft and gap width, the resonant wave frequency shifts to higher values whereas the resonant wave height inside the gap decreases as water depth increases. The amount of reduction of wave height is found to be dependent on the depth to draft and gap width to breadth ratios. It is observed that the effect of water depth on resonance frequency is very small when the ratio of water depth to body draft is equal to or greater than six, while the effect of water depth on resonant water level diminishes when this ratio increases beyond 10. Furthermore, it is observed that the variation trends of the resonant frequency and the reduction of the resonant wave height with water depth are similar at different drafts and gap widths. The present results suggest that the water depth, body draft and the ratio of water depth to body draft are the key factors that influence the resonant responses. It is also found that the potential flow model not only over-predicts the resonant wave heights but also fails to predict the variation trends of the resonant wave height with water depth.