*5.1.1. One-dimensional tsunami*

We examine here how a simple one‐dimensional wave approaching normally to the coast behaves when it encounters a steep continental slope starting from depth 1000 m at a distance of 70 km from shore and sloping upwards to depth 100 m, at a distance of 50 km from shore. How do both height and orbital velocity change as they traverse this shelf? How much is transmitted across the shelf and how much gets reflected? On the return of the ray reflected by the coast, is there a second reflection going back toward shore? Answers to these questions are provided by Video 2 that can be viewed at http://bit.ly/29nKuLh Elapsed time in minutes is given in each frame of the movie. Colors represent the wave height (blue) and the orbital velocities (red). The coast was taken to be a Neumann reflecting boundary, that is, velocity stops perpendicular to the coast, where its magnitude is zero. The bottom profile including the shelf is shown as the heavy black curve at the top in the video. We note several points indicated by the video:

**•** The normalized height wave and orbital velocity wave come in from the right, toward the coast at the left. For this exact solution, the orbital velocity grows much faster than height as the wave advances onto the shallower shelf. This also follows from the Green's Law approximation given by Eqs (6) and (7), which indicates that height depends on depth *d* as *d*−1/4, while velocity varies as *d*−3/4.


It is from the output files of this one‐dimensional simulation that we deduced the transmission coefficient cited in Section 2.4, which was compared with predictions from the Green's Law approximation.
