Introducing this relation in equation 2-47, the relationship for the wave 

 periods is 



(TcL = l;"(Tc) ■ (2-"^) 



Since equation 2-43 applies to any point in the model, and therefore for 

 points on the input line, and if n, is the surface elevation at the 

 line. 





(2-51) 



Equations 2-49 and 2-51 are the two conditions for similarity between 

 model and prototype. The transference equation for velocities is obtained 

 by combining equation 2-29 and the dimensionless variables X = x/L^, and 

 $ = 4iTj,/L^, where it can be shown that 



Tf ^ 3X f2-52) 



and 



^^) = (l^;^ • t2-53a) 



Also, since the model is to be undistorted in scale, 



"57) ' fy ■ (^-=^) 



An alternate relationship can be obtained by introducing equation 2-47, 

 where 



fk'i " {A'i ■ 



(2-54) 



The above results were derived supposing that the particle velocities 

 and the steepness of the waves are small. However, for the validity of 

 the results, these restrictions are unnecessary. The transfer numbers 

 for the periods, the surface elevations, and the particle velocities 

 were developed for situations where the bottom friction is negligible. 

 In models with a small linear-scale number L , friction can attain 

 appreciable values near the coastal areas, in which case the runup and 

 reflection will not be properly reproduced. Also, the potential theory 

 derivation specifically and tacitly excludes the incidence of breaking 



40 



