and equation (4- 17a) becomes 



tanh 





tanh 



\ 



These equations show that, for intermediate -depth waves, the velocity 

 and time ratios are dependent on the local prototype relative depths, 

 the horizontal scale, and the distortion factor. Thus, for wave periods 

 and depths such that 0.05 < d/X < 0.5, scale distortion has the effect 

 of distorting the wave refraction patterns compared with the prototype 

 patterns and those obtained from models with undistorted scale. 



Distorted-scale models of waves that fall within the category of 

 intermediate-depth waves can be used to obtain the correct refraction 

 patterns as the waves approach a harbor, but then the accuracy of the 

 resonance conditions within the harbor basins is sacrificed. The refrac- 

 tion patterns in a distorted-scale model and the prototype will be sim- 

 ilar if 



dn. d„ 



^ = ^ (4-18) 



p m 



and 



Since 



Xp = ttV X„ . (4-20) 



(H 



X = ^ ,a„h^ (4-21) 



n 



V^ tanh -^ (4-22) 



ZTT X„ 



and, in accordance with equation (4-18), 



2'rd^ 

 tanh -^^^ . (4-23) 



211 



