The generation of tsunamis by earthquakes and their consequent run-up on sloping beaches poses engineering problems of site location and design criteria. A formulation is made of the hydrodynamic problem of wave propagation and run-up perpendicular to a sloping beach that is suitable for digital computer calculations. The inclusion of the kinetic energy of the vertical components of velocity permits solitary waves to propagate and the inclusion of an energy dissipating mechanism permits the formation of bores or shocks. A finite element formulation suitable for numerical analysis is presented which includes the effect of bottom friction. Results of digital computations are presented for the propagation and run-up of solitary waves and of tsunami-type waves.
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Heitner et al. (1970) studied this question.