To understand the engineering implications of possible waverun-up resulting from tsunamis, a formulation of the run-up processcapable of giving quantitative answers is required. In thisthesis, a new mathematical run-up model suitable for computerevaluation is proposed and tested. The two-dimensional model usesa flow constrained so that the horizontal velocity is uniform in depth.However, unlike the usual shallow water theory, the terms representingthe kinetic energy of the vertical motion are retained. It isshown that this formulation allows a solitary-like wave to propagateas well as giving a more accurate indication of wave breaking. An'artificial viscosity' term is used to allow the formation of hydraulicshocks. The effects of bottom friction are also included. Themodel is derived for a linear beach slope, in Lagrangian coordinates.A finite element formulation of the problem is derived that is suitablefor digital computer evaluation.
Calculations with the model agree satisfactorily with experimentalresults for the fun-up of solitary waves and bores. The modelis used to obtain run-up data on tsunami-like waves, which show the danger of large run-up from low initial steepness waves on shallow slopes.However, the data also show that bottom friction values cansignificantly attenuate run-up, especially on shallow slopes.
Waves generated by a dipole-like displacement of the simulatedocean floor show that the run-up is usually larger when the upwardsdisplacement is nearest the beach than when the downwards displacementis nearest the beach.
