Dimensional analysis on piston-mode narrow-gap resonances of two fixed side-by-side barges under Stokes waves

A dimensional analysis is presented for piston-mode resonant fluid response between two identical, fixed, side-by-side barges subjected to Stokes waves. Based on a simplified physical model, the key parameters governing the resonant response of the water column confined in the gap are identified. For a two-dimensional deep-water, wave-only configuration, wave steepness and draft-to-beam ratio are found to be the two principal non-dimensional parameters. Numerical simulations are performed in a fully nonlinear wave tank over a range of these two parameters. As the draft-to-beam ratio increases, the non-dimensional resonant wave amplitude within the gap rises monotonically and then remains almost constant beyond a certain value. For the considered wave steepness, the resonant response tends to be inversely proportional to the wave steepness owing to the quadratic nature of the damping. To this end, a physics-based empirical formula is subsequently derived to provide a convenient tool for rapid estimation of resonant fluid response in the considered configuration. Although the accuracy of this empirical formula depends on the ranges of the governing parameters covered in the numerical simulations, it demonstrates fairly satisfactory agreement with other existing experimental and numerical results within similar parameter ranges. It is expected that the present approach can be extended to three-dimensional gap resonance problems between two barges where other modes of resonance are predominant.