Third-order interactions, wave run-up and hydrodynamic loading on a vertical plate in an infinite wave field

• The wave run-up and the hydrodynamic loading exerted on a vertical plate are considered.
• Two approaches are taken assuming incident waves in confined and infinite wave fields.
• Both methods account for third order interaction phenomena.
• The infinite wave field approach assimilates the plate as a degenerated elliptical cylinder.
• The numerical predictions demonstrate that the wave reflections from the lateral walls in a confined field could be significant.

The nonlinear wave interaction problem with a vertical plate of finite length is considered. Reference is made to previous experimental and numerical studies reported in Molin et al. [1–3], where it was shown that the observed run-up phenomena are due to third-order (or tertiary) interactions between the incoming and reflected wave systems. In this paper a new numerical model is proposed where the presence of lateral walls is relaxed. Run-up computations, with and without confinement effects, are compared. It is found that, in the model tests reported in Molin et al. [3], the effect of confinement was relatively small. The time-varying and steady wave loads which are exerted on the plate are also investigated. The dedicated numerical predictions show that as the wave steepness is increased the response amplitude operators of the time-varying loads first increase, reach a maximum and then decrease dramatically, due to phasing effects.