Analytical and numerical studies of resonant wave run-up on a plane structure

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Wave run-up is the vertical extent of wave up rushed on a structure. To describe wave run-up characteristic, we tend to relate to its maximum height. It was a common belief that the leading wave will usually reach the maximum run-up. However, It turns out that this is not always the case. Resonance is a phenomenon when the incident wave shares the same frequency as the natural frequency. In this article, the natural frequency of a semi-enclosed basin on a plane structure is derived using the variable separation technique. Next, the staggered conservative scheme is used to test these natural frequencies through simulations of wave run up on a plane structure. The result shows that when the incoming wave frequency is close to the natural frequency, the largest run-up height is not the leading wave, but the second, third, or fourth waves. This indicates the occurrence of resonance phenomena. Sensitivity analysis was applied to show the dependence of the maximum run-up height to the structure’s slope, as well as the incident wave frequency. Further, a physical simulation was conducted to examine whether the resonance phenomenon appears in the actual events.