efficient calculation of waves transforming under combined diffraction, 

 refraction, and shoaling to break is required to obtain realistic predictions 

 of shoreline change in such situations. 



140. Figure 11 is a definition sketch of the calculation procedure for 

 the breaking wave height and angle behind a structure (Kraus 1981, 1982, 

 1984). Conceptually, the area of interest is separated into a shadow region 

 and an illuminated region by a wave ray directed toward the beach from the tip 

 of the structure at the same angle as the incident waves arriving at the tip. 

 To determine the breaking wave height, a diffraction coefficient must be 

 calculated in both regions because the diffraction effect can extend far into 

 the illuminated region. To determine the breaking wave angle, inside the 

 shadow region, wave rays are assumed to proceed radially from the tip of the 

 structure T? 1 at an angle d 1 to arrive at some point P 2 , where they 

 break. 



141. The angle 9 1 at which a wave ray must start to arrive at P 2 

 inside the shadow region is not known a priori since it is a function of the 

 breaking criterion as well as the distance alongshore defining the location of 

 grid cells in the numerical calculation. A ray shooting technique can be used 

 to determine X (Kraus 1982, 1984), but this procedure is complex and 

 requires considerable execution time. As an approximation, the geometric 

 angle 8 & defined by the straight line between P x and P 2 is used. 



142. In areas affected by diffraction, Equation 18 is used to calculate 

 the height of breaking waves that have been transformed by diffraction, 

 refraction, and shoaling 



H b = WDbW (18) 



where 



K D = diffraction coefficient 



6 D = angle between incident wave ray at P x and straight line 

 between P x and P 2 , if P 2 is in the shadow region 



H b = breaking wave height at the same cell without diffraction 

 The diffraction, refraction, shoaling coefficients are also functions of the 

 depth at P x and the wave period, but these quantities are known and, there- 

 fore, not included in the function arguments in Equation 18. 



67 



