stability o£ armor units, as a function of Reynolds niomber, have been 

 conducted (see Sec. VI, 3, c). In tests where the reflection of waves 

 from, and the transmission of waves through, rubble-mound structures 

 are studied, the scale effects also vary with Reynolds number. Studies 

 to determine model design procedures to minimize the scale effects have 

 been discussed by Le Mehaute (1965); the results of tests concerning this 

 aspect of model design were also reported by Keulegan (1973). 



Since the velocity, V^^, of the waves or of the water particles that 

 impinge on armor units during wave attack are not easily measured during 

 the conduct of breakwater stability tests, V,^ can he conveniently elimi- 

 nated from equation (6-lc) by the relation V^ = f(gH)-'-/^. Other helpful 

 substitutions are v = y/p„, Ya = Pag> ^^^ (^c^a = ^v^^a/>'a) ^''^' 



where 



V = kinematic viscosity 



Y„ = specific weight 



k = shape coefficient such that W = k"^Y (Z )^. 

 v ^ a v 'a^ c^a 



After making these substitutions, equation (6-lc) becomes 



,1/3h 



(^a/Tw - ^>l" 



f" 



>1/2h1/2 (H H d (^ 



,a,|3, A, 0,D 



(6-3a) 



Considering that the model structures would be constructed geometrically 

 similar to hypothetical or proposed prototype structures; assuming that 

 the model structure and wave dimensions are such that the Reynolds number 

 is large enough to render the viscous forces negligible, and that the 

 surface texture of the model armor units are sufficiently smooth, relative 

 to that of the prototype units; and then recognizing that the shape of 

 armor unit. A, and the manner in which armor units are placed in the 

 cover layer of the structure (placing technique, P^) are important parts 

 of the condition of geometrical similarity (relatively small variations 

 in placing technique can cause relatively large variations in the stabil- 

 ity of armor units), and that the seaward slope of the breakwater, wave 

 absorber, or jetty face, ct, is an important variable in both the sta- 

 bility and cost of the structure, the basic equation used for guidance in 

 the testing of specific or hypothetical structures reduces to 



yl/'H 



(-^a/Tw - ^yj' 



- (f> 



X' 



a, A, e, p, 



..-) 



(6-3b) 



This relation is the same as that used by Hudson (1958) in a general test- 

 ing program to determine the function f ' ' ' ' for an idealized breakwater 



319 



