and from equation (240), 



, 2d sin a da 



' Jx (248) 



cos a S sin 2 a^ 



Using equation (239) to define x and substituting equations (247) and 

 (248) into equation (246) , it becomes 



I 



tt/2 2 d , 



s sin a dx 



S sin 2 a, /g~ f~ / d sin 2 a d 



Collecting terms, 



which gives 



a l '.** ' f " I 

 d + S 

 V s \ 



2 /d~ C*l 2 



(249) 



s s 



S sin 2 a. 



S sin a, /g Ja 



I 



da (250) 



2 /T 



t 2 \. . (2S1) 



S sin a-^ /g 



Shen and Meyer (1967) and Shen (1972) give a solution for curved 

 coastlines. For a circular arc, wave trapping can be defined using the 

 equations 



rd0 . , 2 2 „2-\-l/2 f2S21 



tan a = = ±(n z r z - c') x ^ L^^^J 



dr 



and 



n tanh 



m i - 



(253) 



where 



r = the radius of curvature of a contour line (taking circular 

 bottom contours to define the shelf around the coastline) 



= the coordinate angle in polar coordinates of a point along 

 the wave ray at radius r 



c = a constant 



n = a variable along the wave ray 



d = the water depth at radius r 



n = 1, 2, 3. . . defines an integer number of wave crests around 

 a circular island 



116 



