General solutions for the initial run-up of a breaking tsunami front

An assessment of potential damage on coastlines due to tsunami requires prediction of the likely flow depths and impact forces on structures. Since tsunami have a long wavelength relative to the water depth, models that solve the non-linear shallow water equations (NLSWE) are appropriate. Carrier et al (2003) presented solutions for tsunami that do not break. However, where the leading front of the tsunami breaks, the wave front is more similar to a bore approaching the shoreline. An analytical treatment for the run-up driven by an incident bore was developed by Shen & Meyer (1963). However, the Shen & Meyer result is only unique close to the shoreline, and the flow depths and velocities depend on the seaward boundary condition. Here, a new numerical model is presented that solves the NLSWE for the case of a broken tsunami front arriving at the shoreline. It is a simple model that allows specification of either the flow depths or velocities at the seaward boundary, and the solution method allows the effects of friction to be incorporated. The model is able to reproduce the Shen & Meyer analytical solution for the initial motion of the shoreline. The potential damage to coastal structures and other infrastructure may be assessed by calculation of impact and drag forces due to the predicted flow depths and velocities