This paper is intended to study impact forces of breaking waves on a rigid wall based on a nonlinear potential-flow theory. This is a model problem for some technologically important design issues such as the impact of breaking waves on ships, coastal and offshore structures. We are interested in the short-time successive triggering of nonlinear effects using a small-time expansion. The analytical solutions for the impact force on a rigid wall and the free-surface profile are derived.
There is a long history of experimental and theoretical studies to determine impact forces acting on a rigid wall, which is suddenly started from rest and made to move towards a fluid taper. The problem is motivated by the impact of breaking waves on ships, coastal and offshore structures, which is one of the most severe environmental loads on structures. The impact due to a breaking wave striking a wall is of high intensity and short duration. This is attributed to the direct collision between a fluid and a wall surface. The direct collision of a breaking wave with a wall generates an impulsive pressure on the wall. This is similar to the problem of initial-stage water impact. Unfortunately, existing wave theories based on small- and finite amplitude assumptions cannot be directly adopted to evaluate the breaking wave force on a wall due to the highly nonlinear and transient nature of the problem. In reviewing the previous studies, one of the most important and unresolved questions is how the initial stage of the breaking wave impingement on the wail can be properly characterized and simulated. Cumberbatch (1960) considered the case of symmetric normal impact of a water wedge on a wall and Zhang et al. (1996) extended his work to an oblique impact.