which shows that the roughness scale is a fimction only of the linear 

 scale-distortion ratio. In terms of the Manning roughness n 



H^ 



N 



2/3 



(3-9) 



1/2 



This can be stated in terms of the distortion ratio DF = (Ly) /(Lh^ ^^ 

 follows : 



. = Lvr_ VZll_ = F;?2/3 a . Y2/3-1/2) 



= DF -^'^ (l, V^ 



n^ = DF2/3(l^)1/6 (3_io) 



listortion on the rough; 



H Mr 5? 



The effect of scale distortion on the roughness ratio can now be shown 

 as follows : 



1/100 



1/100 



1 



0.464 



1/100 



1/1,000 



10 



1.47 



1/100 



1/2,000 



20 



2.08 



Thus, the higher the degree of distortion used in the model, the greater 

 the roughness which is required in the model. For large distortions, 

 boundary roughness alone may not yield a sufficient model roughness. 

 Then, it is necessary to use some type of vertical roughness element 

 which extends throughout the entire water depth. 



Keulegan (1951, 1966) has shown that, in distorted-scale models of 

 mixed estuaries, the salinity (or density) ratio should be unity. That 

 is 



Sr or p^= 1 . (3-11) 



However, Harleman (1971) states that, whereas the salinity scale should 

 be unity for models of highly stratified estuaries, there is no strict 

 necessity for this scaling in models of mixed estuaries. The general 

 requirement, based on the Richardson number, is that 





(3-12) 



This requirement is most conveniently satisfied by using a density ratio 

 of unity (the general practice) . 



54 



