A new semi-analytical solution for gap resonance between twin rectangular boxes

Abstract

This study gives a semi-analytical solution for gap resonance between twin fixed, partially immersed rectangular boxes based on the linear potential theory. The fluid region between and below the boxes is treated as dissipative domain. A new method is proposed to introduce energy dissipation into the dissipative domain by adding the artificial resistance force. Two different dissipative boundary conditions are imposed on the gap-free surface and the boundary between the dissipative domain and the non-dissipative domain. A complex dispersion relation is used to describe the wave motion in the dissipative domain with free surface. The newly developed semi-analytical solution is confirmed by previous analytical results, results by independently developed multi-domain boundary element method solution, experimental data and numerical results based on viscous fluid model. A simplified formula is developed to evaluate the resistance coefficient for the dissipative domain. The present model with artificial energy dissipation is simple and efficient and is expected to be valid for more relevant problems.