To determine the variation of wave amplitude with respect to distance 

 from the shoreline, the equation for U is put in the form 



d 2 U 

 dp 2 



(1 + P z ) 



2-v 1/2 



(1 + p^) (1 + p z ) 



2l 2 



U = 



(191) 



where p = x/a. This equation was solved by Hidaka using Stormer's method 

 (see Milne, 1953). The wave profile is defined in Table 1. 



Table 1. Distribution of amplitude U 

 (from Hidaka, 1935b) . 





First 



mode 





Second mode 



x/a 



U 



x/a 



U 



x/a 



U 



x/a 



U 



0.0 



1.0000 



2.0 



-0.7985 



0.0 



1.0000 



2.0 



0.5600 



0.1 



0.9813 



2.1 



-0.7766 



0.1 



0.9474 



2.1 



0.6665 



0.2 



0.9265 



2.2 



-0.7432 



0.2 



0.7964 



2.2 



0.7392 



0.3 



0.8391 



2.3 



-0.6998 



0.3 



0.5668 



2.3 



0.7773 



0.4 



0.7244 



2.4 



-0.6476 



0.4 



0.2868 



2.4 



0.7818 



0.5 



0.5889 



2.5 



-0.5880 



0.5 



-0.0115 



2.5 



0.7548 



0.6 



0.4392 



2.6 



-0.5224 



0.6 



-0.2972 



2.6 



0.6995 



0.7 



0.2822 



2.7 



-0.4520 



0.7 



-0.5445 



2.7 



0.6197 



0.8 



0.1239 



2.8 



-0.3781 



0.8 



-0.7346 



2.8 



0.5200 



0.9 



-0.0305 



2.9 



-0.3018 



0.9 



-0.8566 



2.9 



0.4052 



1.0 



-0.1766 



3.0 



-0.2241 



1.0 



-0.9070 



3.0 



0.2800 



1.1 



-0.3110 



3.1 



-0.1462 



1.1 



' -0.8887 



3.1 



0.1493 



1.2 



-0.4313 



3.2 



-0.0688 



1.2 



-0.8096 



3.2 



0.0176 



1.3 



-0.5357 



3.3 



0.0072 



1.3 



-0.6807 



3.3 



-0.1110 



1.4 



-0.6233 



3.4 



0.0810 



1.4 



-0.5149 



3.4 



-0.2327 



1.5 



-0.6936 



3.5 



0.1521 



1.5 



-0.3256 



3.5 



-0.3443 



1.6 



-0.7466 



3.6 



0.2197 



1.6 



-0.1261 



3.6 



-0.4430 



1.7 



-0.7827 



3.7 



0.2834 



1.7 



0.0716 



3.7 



-0.5267 



1.8 



-0.8028 



3.8 



0.3428 



1.8 



0.2572 



3.8 



-0.5940 



1.9 



-0.8076 



3.9 



0.3975 



1.9 



0.4221 



3.9 



-0.6436 







4.0 



0.4473 







4.0 



-0.6754 



************* EXAMPLE PROBLEM 12 * 



******** 



GIVEN : Water depth, d g , at the toe of a nearshore slope is 30 meters; 

 the distance a = 12,430 meters (7.72 miles). Complete reflection occurs 

 at the nearshore slope, and it can be assumed to behave as a vertical 

 slope. 



93 



