Defining A = ea where e is an arbitrary increment, 



d-j cL; d + jS ea 



B . D , = -*■ = -^ - 



«* " A ea 



w = s 



_e(/2 - 1) 



ea 



■ th 



at the j increment. 



The equations of Wilson (1972) can then be expressed as 



\s( 1 



+ J 

 1) 





\ 



)-. 



- u. 



J 



K 2 (/2~ - 



«> 



J + l 



K 2 (v^" - 1) e(*^ - 1) 



+ j * 1 



::: 2(it)2 £ \/N. + N.\ 



(201) 

 (202) 



(203) 



(204) 



************* EXAMPLE PROBLEM 14************** 



GIVEN : The water depth, d s , at the toe of a nearshore slope is 30 

 meters; the slope of the shelf is S 2 = 0.001. Complete reflection 

 occurs at the nearshore slope. 



FIND : The wave profiles using the methods of Hidaka (1935b) and Wilson 

 (1972). 



SOLUTION : From example problem 12, 



(/2 - 1) d (/2 - 1) 30 



0.001 



= 12,430 meters 



T = 3.2417 



Wi 



2,350 seconds 



T 2 = 1.9254 



'gd 



1,395 seconds 



Exploring the second mode of oscillation as before, and using values of 

 A = 0.1 a = 1,243 meters (4,078 feet) 



97 



