which is the well-known Green's Law. Noting that r\ max = a, the amplitude, 

 equations (42) and (45) can be written as 



ag 



1/2 



|l/2 



aL 



(50) 

 (51) 



For the unrefracted wave, noting that 



a H„ 

 2 2 



(52) 



W /g_\ 1/2 \ d 2/ \ d 2/ 



(53) 



Also, 



3/4 



( 2 " d ) 2 



,1/4 / . vl/2 , , 

 d l\ / d 2\ / d l 



(54) 



(55) 



3/h 



(56) 



Equations (49), (54), and (56) provide a simple, first-order solution 

 for the shoaling of an unrefracted, small -amplitude, shallow-water wave. 



************* EXAMPLE PROBLEM 2 



************** 



GIVEN: A long wave with a period of 20 minutes and a height, H, of 

 0.4 meter (1.31 feet) passes from a 1,000-meter (3,280 feet) water 

 depth into a 500-meter (1,640 feet) water depth. The wave is assumed 

 to be nondispersive. 



42 



