Analytical and numerical study of nonlinear effects at tsunami modeling

Numerical Study of Tsunami Waves with Sloping Bottom and Nonlinear Friction

“…For the case with an even bottom, an analytical solution to the problem has been derived (see [21]), while for the case with sloping bottom, a finite difference method has been developed for solving the problem numerically. The numerical technique has also been used to investigate the propagation of the long waves and the effect of nonlinear friction.…”

“…In the area which is far from the source of tsunamis, the variable depth as well as nonlinear friction will influence the wave evolution [21]. For the case where the undisturbed water depth is a linear function of the horizontal x coordinate as shown in Figure 1.…”

“…The duration of a typical tsunami is 5 -100 min, with wave length between 100 m and 1000 km, and propagation speed 1 -200 m/s. Tsunami wave heights can be up to tens of meters [21] . The popular models to describe the tsunami wave propagation are based on the various approximations of a shallow water system.…”

“…Tsunami waves are defined as long-period waves created by large scale short-term perturbations such as underwater earthquakes like the 2004 Indonesian earthquake [21] , the 1969 Portuguese Tsunami [4] , and the 1968 Tokachi-oki Earthquake [6] , eruption of underwater volcanoes, for example, the 1883 Krakatau Volcano eruption [21] , landslides, for instance, the 1929 the Grand Banks landslide [3] , rock falls, pyroclastic avalanche from land volcanoes entering the water, asteroid impact, underwater explosion, etc. The duration of a typical tsunami is 5 -100 min, with wave length between 100 m and 1000 km, and propagation speed 1 -200 m/s.…”

“…The shallow water theory in Cartesian coordinates, when no rotation is applied, is used to simulate long wave propagation. The governing equations are as follows [21] :…”