ik X -ik X 

 5 = a.e + a e 



X > i 

 — s 



(85) 



i — ik X -ik X 

 'f- (a.e -a e ) 



where a^ is the amplitude of the incident wave, which without loss o£ 

 generality may be taken to be real, and a^. is the complex amplitude of 

 the reflected wave. The wave number, k^ = 2it/L, where L is the_ wave- 

 length of the incident wave, is given by 



(863 



w. 



On the rough impermeable slope, <_x <_ i^, the effect of bottom 

 friction is retained and equation (80) may be written 



8? 



ia)(l-if ) 8x ' 



< X < 



(87) 



when equations (83) and (84) are introduced. 



Multiplying equation (87) by h to obtain an expression for 9(uh)/Sx 

 and introducing this in equation (79) yield the governing equation 



^^^W 



^ a-i%) 



C = 



< X < £ 

 — — s 



(88) 



With the depth varying linearly on the slope, i.e.. 



h = X tan^ 



< X < a 

 — — s 



(89) 



equation (88) is seen to be a special form of the Bessel Equation 

 (Hildebrand, 1965) with the solution 



C = A J (2 

 t 



■(l-if^)x 

 g tanB 



< X < £ 



(90) 



50 



