cells measuring 0.25 and 0.20 m in the x- and y-directions, respectively, were 

 used for the simulation. The center of the shoal was located at the point 

 with x- and y-coordinates of 15 and 10 m, respectively. The equation de- 

 scribing the outer extent of the shoal is given by 



(f) 2 * ft? 



2 /...\ 2 



= 1 (50) 



where x 1 and y' denote a local coordinate system whose origin is located 

 at the center of the shoal. Also this coordinate system is rotated 20 deg in 

 the clockwise direction relative to the x- and y-coordinate system. All length 

 scales for both coordinate systems are measured in metres. Water depths, de- 

 noted by h and measured in metres, were calculated from the following three 

 equations, 



h = 0.45 for y' > 5.84 (51) 



h = 0.45 - 0.02 (5.84 - y')(outside the shoal boundary) (52) 



|1/2 

 h = 0.45 - 0.02 (5.84 - y 1 ) + 0.3 - 0.5 

 (inside the shoal boundary) 



%fl 



If 1 ) -\f„ 



An incident wave with a period of 1.00 sec, a height of 1.06 cm, and a direc- 

 tion of approach parallel to the x-axis was used as the deepwater boundary 

 condition for the simulation. 



47. Figures A2 through A4 show comparisons between the experimental 

 data (open circles) and model results (solid line) for all eight profiles. 

 Results are presented as profiles of relative wave height (observed wave 

 height divided by incident wave height). A refraction analysis (presented in 

 Berkhoff, Booy, and Radder (1982)) shows that a caustic occurs at a point be- 

 tween profiles 2 and 3. Results show that the model is quite capable of accu- 

 rately simulating diffractive effects at, and beyond, the caustic location. 

 Consequently, it is a much more powerful tool for simulating wave transforma- 

 tion than refraction theory alone. Berkhoff, Booy, and Radder (1982) and 

 Kirby (1983) also numerically simulated this experiment in order to test their 

 parabolic approximation models. Accuracy of their model results, using linear 

 wave theory, is comparable to that obtained using RCPWAVE. Results obtained 



28 



