For this example, the shelf needs to extend 10,000 meters from the 

 toe of the shoreline slope to have the wave ray turn parallel to the 

 bottom contours. The wave ray which was reflected from the shoreline 

 will impinge upon the shoreline again at a point 51,400 meters (31.94 

 miles) along the coast, provided the wave is trapped. 



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For the particular case of a shallow-water wave on a straight section 

 of coastline and uniform shelf slope, given by equations (237) and (243) 

 and illustrated in Figure 35, as the angle a 1 decreases the distance of 

 the caustic from the shoreline increases and the distance y between the 

 point of reflection and the point where the wave ray impinges again on 

 the coastline also increases. 



When the tsunami energy becomes trapped between a caustic and a 

 coastline, the energy will tend to propagate along the coastline. This 

 will excite longshore edge waves along the coastline, and may substan- 

 tially increase observed wave heights. When the coastline is irregular, 

 the trapped waves may concentrate their energy at particular coastal 

 points. An investigation of the wave rays using the usual wave refraction 

 techniques will define the caustic locations, and the locations of any 

 coastal points where energy concentrates. 



Tsunamis generated in coastal areas may have part of their energy 

 trapped along the coastline, as waves radiating away from a source area 

 may become trapped within a caustic in the same manner as reflected waves. 

 For a wave ray originating within the coastal area, d s is the water 

 depth at the point of origin, Xp the distance seaward from the point of 

 origin, and o^ the angle between the wave ray and the orthogonal to the 

 bottom contours as before. This is illustrated in the following example 

 problem and in Figure 37. 



Edge of Shelf 



Figure 37. Trapping of generated tsunami. 



113 



