The fate of the energy, momentum, and volume (or mass) of the leading-elevation N-type tsunami considering geophysical scale is studied. From the epicenter to the land the physical properties of the positive wave of tsunami are calculated using a second order depth integrated model. Not only the incident wave characteristics but also the scale and shape of bathymetry are very important for the propagation of tsunami physics.
Tsunami is caused by undersea earthquake and usually propagates across the entire ocean. Tsunami is not detected well over deep and intermediate ocean area due to its very long length and small crest amplitude. As tsunami enters shallow coastal region, its wavelength reduces and the amplitude increases, which is believed to lead low altitude inland around coast to catastrophic inundation damage. For decades, various aspects of tsunami propagation have been studied experimentally, numerically and theoretically. Because the inundation is directly related with water surface elevation, interests have been focused on water surface elevation of tsunami. For example, Synolakis (1987) presented an analytical model for non-breaking solitary wave runup on plane beach. Briggs et al. (1995) presented intensively measured data of solitary wave runup heights around a circular island in laboratory scale. Matsuyama et al. (2007) carried out relatively undistorted experiment on the shoaling and fission of tsunami. Considering the complexity in real fluid motion and bathymetry, numerous numerical models based on shallow water equation (Titov and Synolakis, 1995; Li and Raichlen, 2002) and Boussinesq equation (Goring, 1987; Fuhrman and Madsen, 2008; Lynett, 2007; Kim and Lynett, 2012; Kalisch and Senthilkumar, 2013) have been developed and applied.
Based on many analytical, experimental and numerical studies, it was proposed that the runup height and amplification of nonbreaking wave generally increased as the bottom slope was milder (Synolakis, 1987; Suh et al., 1997; Li and Raichlen, 2002). In field experience, however, tsunami damage has not been frequently reported where a continental shelf with very gentle slope existed, for example, the sea of north Australia, east China and west Korea. On the contrary, east coast of Japan, India and Sri lanka where the under sea bathymetries are relatively steep have experienced severe tsunami attacks. Recently, Madsen et al. (2008) and Kim and Son (submitted) studied on the contradictory results: They examined the importance of geophysical scale for the tsunami wave study and proposed that unrealistic wave could be developed under improper scale and geometry considerations. For the damping by friction Horsburgh et al. (2008) found that the frictional dissipation was not primarily responsible for tsunami attenuation using a numerical model on tsunami crossing ocean and continental shelf. This implies the damping could be resulted by the geometry of geophysical scale, not by frictional effect.
