Propagation of obliquely incident tsunamis on a slope part I: Amplification of tsunamis on a continental slope

A new analytical solution of tsunami which is obliquely incident on a continental slope is derived based on the linear shallow water wave theory. The model of a continental slope consists of a finite constant slope and a bottom of uniform depth and has a vertical wall at the shoreline. Because of the existence of the vertical wall, another function can be taken as one of the fundamental solutions on a slope in addition to the confluent hypergeometric function M. Based on the solution obtained, the characteristics of tsunami amplification on a continental slope are discussed in terms of the conditions of the incidence. The magnitude of the amplification can be predicted with several parameters of wave incidence, such as, the incident angle and the relative incident-wave length to the topography. Especially, when a tsunami is incident almost parallel to the slope, we found that there exists distinctive amplifications for particular parameters characterizing the incident wave. The effect of the existence of the vertical wall is also discussed. The characteristics of amplification also depend much on the position of the vertical wall.