shoaling were always greater than given by linear theory which was consis- 

 tent with the one-dimensional tests above (Fig. 85). Refraction coefficients 

 for the a = 30° and 45° tests are shown in Figure 89. Unprimed values 

 are based on angles calculated by Snell's Law. The numerical model showed 

 less departure from linear theory at 30° than at 45°. It was concluded 

 that wave refraction techniques based on linear theory (Snell's Law) do 

 not accurately predict the behavior of nonlinear dispersive waves in shoal- 

 ing and refraction. Regarding wave refraction, it was also concluded that 



"The lack of similar laboratory and field work inhibits 

 the range of conclusions that can be drawn from these 

 results (Hebenstreit and Reid, 19 78, p. 95). ^6 



The limited comparisons between Snell's Law and laboratory measurements 

 shown by Wiegel (1964)^^ exhibit systematic differences and wide scatter 

 in some instances. 



It would now appear that these measurements made in the 1950 's must 

 be supplemented by more sophisticated experiments to verify the new numerical 

 models of the 1980 's. 



-L.U 







•H 



U 

 •H 

 <4-l 



0) 



o 

 o 





.^^J^""""^--^^^^^^^^kJ(30) ^^~— . 



c 

 o 



Ii).9 

 o 



CO 

 M 





^"""-^v,^^^^ ^^^"^--<:K^5) 



(U 

 U 





KjASr""--^.^^^^^^^ 



u 







50 



40 

 Depth (m) 



30 



Figure 89. Comparison of pure wave refraction coefficients by numerical 

 model and linear wave theory (Snell's Law) (after Hebenstreit 

 and Reid, 1978). 



''^HEBENSTREIT and REID, op. ait. 

 22wiEGEL, op. oit. 



219 



