3. Diffraction, 



The diffraction solution (in the lee of the structure) used in the model 

 is based on the method of Penny and Price (1952). Assumptions used in this 

 method include a semi-infinite breakwater, which is infinitesimally thin, 

 linear wave theory and constant depth. A definition sketch for wave 

 diffraction is shown in Figure 3. The quantity THETAO represents the angle 

 of wave incidence relative to the jetty axis, ANGLE represents the angle from 

 the jetty at the point where the diffraction coefficient is to be computed, 

 and RAD is the radial distance. The radial distance is then cast into a 

 dimensionless parameter, RHOND (= 2^ RAD/L), where L is the wavelength. This 

 is equivalent to multiplying the radial distance by the wave number k. 



The diffraction coefficient AMP is expressed as the modulus of the 

 diffracted wave 



AMP 



(Sum 1)2 + (Sum 2)2 



(17) 



where 





Sum 1 



= [cos ( 





[sin ( 





[cos ( 





[sin ( 



Sum 2 



= [cos ( 





[sin ( 





[cos ( 





[sin ( 



RHOND (cos (ANGLE-THETAO)) 



RHOND (cos (ANGLE-THETAO)) 



RHOND (cos (ANGLE+THETAO)) 



RHOND (cos (ANGLE+THETAO)) 



RHOND (cos (ANGLE-THETAO)) 



RHOND (cos (ANGLE-THETAO)) 



RHOND (cos (ANGLE+THETAO)) 



RHOND (cos (ANGLE+THETAO)) 



(^ (1.0 + Cp + S))] + 



(- 2 (S - Cp))] + 



{\ (1.0 + Cp + S))] + 



(2 - (S - Cp))] (181 



(- I (S - Cp))] + 



{\ (1.0 + Cp + S))] + 



(- 2 (S - Cp))] + 



{\ (1.0 + Cp + S))] (191 



In Equations (18) and (19), Cp and S represent Fresnel integrals and are 

 computed in the model by means of an approximation after Abramowitz and 

 Stegun (1965). 



Having obtained AMP, the wave height at the location in question is 

 simply the product of the specified partially refracted incident wave height 

 and AMP. The angle of the wave crest is computed assuming a circular wave 

 front along any radial; this angle is then refracted using Snell's law. 



Throughout the refraction and diffraction schemes, the local wave 

 heights are limited by the value, 0.78 x depth. 



16 



