Suppression of the second harmonic induced wave near-trapping around a cylinder array

Near-trapping is an essential resonant phenomenon associated with multiple-column structures in water waves, which exhibits high wave profiles in the area enclosed by multiple columns. For engineering safety, a straightforward scenario is proposed in this study to suppress the near-trapping phenomenon by allowing the multiple columns to move longitudinally with respect to the symmetric axes. To evaluate the effectiveness of the scenario, a stable and efficient second-order numerical model in the time domain is developed and adopted, which is also robust for the simulation of multiple structures with complex geometry and undergoing individual motions. Since both the first-order and second-order boundary value problems are solved, the second-order nonlinear properties are highlighted and the second harmonic induced near-trapping is the main focus of this study. For the cases in this study, the numerical results obtained by the validated numerical model confirm that this scenario can reduce the maximum second harmonic of the wave elevation by 63% and the maximum second-order wave elevation by 59% at the second near-trapping frequency. The first-order wave elevation is also reduced, and it is even smaller than the incident wave in a large portion of the enclosed region. As a mass–spring system is considered in the simulation of body responses, by testing different body masses and stiffnesses, it is revealed that the wave profile is insensitive to those parameters and the reduction in the wave profile occurs for all those parameters tested. It is interesting to find out that the near-trapping frequency can shift in the suppression scenario, and a remarkable reduction (32%) in the second-order wave elevation is still observed at the shifted near-trapping frequency.