The energy per meter length of wave crest is 



E. = 



I H j L j _ 10, 055(0. 5) 2 75,100 



E r = 



= 2.36 x io 7 kilogram-meters per second squared 

 = 2.36 x 10 7 joules 



10, 055(0. 31) 2 75,100 



Y H z L 

 r v 



= 9.07 x lo b joules 



T = /9.8 x 3,025 (40 x 60) = 413,000 meters 



L t = C 2 T = V 



Y H t L t 10,055(0.16) 2 413,000 



E = = 



t R R 



1.33 x io 7 joules 



As K^ is negative, i.e., the reflected wave is out of phase, then 

 for energy to be conserved 



E. 



E. - E 



2.36 x io 7 - 9.07 x io 6 = 1.45 x IO 7 joules 



compared to the computed value of E^ = 1.33 x io 7 joules. The differ- 

 ence results from the minor errors which occur using Figure 20. 



3. Nonlinear Depth Transitions. 



Kajiura (1963) investigated waves passing from deep water to shallow 

 water over the nonlinear slope profile shown in Figure 21. The profile 

 is defined by the equation 



iw = Hi + k) ~ Hfc ■ i) tanh 



(175) 



where the effective slope length 



I is given by 



- 2][ 

 n 



(176) 



Lj is the wavelength at depth dj, L2 is the wavelength at depth d£, 

 and n is an arbitrary small number in equation (175) which fits the 

 equation to the actual slope and determines the length of the slope in 

 equation (176) . 



The reflection coefficient obtained by Kajiura is given by the 

 equation 



H. 



:inl YW^), 



inh [fr^)' 



(177) 



