Nonlinear Model of Coastal Flooding by a Highly Turbulent Tsunami

When a tsunami wave comes from ocean and propagates through the shelf, it is very important to predict several dangerous factors: (a) maximum flooding of the coast, (b) tsunami wave height on the coast, (c) velocity of the tsunami front propagation through the coast, and (d) time of tsunami arriving at a given point in the coast and around it. In this study we study the separate case where the angle of inclination α of the seacoast is equal to zero. A linear solution of this problem is unsatisfactory since it gives an infinite rate of the coastal inundation that means the coast is flooded instantly and without a frontal boundary. In this study, we propose a principally new exact analytical solution of this problem based on nonlinear theory for the reliable recognizing these essential tsunami characteristics. The obtained formulas indicate that the tsunami wave can be stopped (or very strongly eliminated) in the shelf zone until approaching the shoreline. For this aim, it is necessary to artificially raising several dozens of bottom protrusions to the level of the calm water.