seiche-type waves which have small wave heights in the prototype. Thus, 

 distorted scales are used when the departure from geometric similarity 

 serves a definite purpose, and the use of the model is limited to those 

 problems for which the resulting scale effects are minor. The accuracy 

 of such models depends primarily on the degree of scale distortion and 

 the prototype water depths relative to wavelength. 



For long, shallow-water waves of small amplitude, and < d/X < 0.05, 

 in which the wave velocity is given by the relation 



V - (gd)l/2 , (4-10) 



distorted-scale models reproduce wave refraction and diffraction and 

 resonant periods accurately. For all types of waves, the bottom- friction 

 effects in distorted-scale models are less than those in undistorted mod- 

 els. Wave reflection effects are increased by scale distortion. For 

 long waves, the velocity scale can be determined directly from equation 

 (4-10) as follows (eq. 2-9, Section II); 



or, since gj„ = gp, and all vertical lengths (Ly) in the model are 

 measured in accordance with the depth ratio; i.e.. 



n 



d 



p H 



Vr = {L,yj^ . (4-11) 



This is the same relationship that is obtained by use of the Froude 

 model law with the water depth as the linear dimension. If the hori- 

 zontal lengths are designated Lj^, the scale of horizontal lengths as 

 '^'^h^m/'^'^h^p "^ f^h^r' ^"'^ '^^^ distortion factor (a number greater than 

 unity) as DF, then 



— ^)r 



DF = )^ . (4-12) 



(Mr 



Based on the designations above, the time ratio is derived as follows: 



^' V, A \l/2 



T = ^ ^' , . (4-13) 



^1/2 

 (DF)^/2 



209 



