2. Reynolds Number . 



Model-to-prototype ratios have often heen designated for model tests 

 because many tests are for specific site conditions. However, evalua- 

 tion of scale effects among a collection of model tests is difficult 

 when using the model-to-prototype ratios because the same model dimen- 

 sions may be modeling greatly different prototype conditions. An 

 example might be comparison of a l:20-scale model with a l:50-scale 

 model, both of which might have the same model dimensions. Direct com- 

 parisons between various model scales are possible by using dimension- 

 less variables, including a Reynolds number, assuming viscosity is the 

 primary cause of scale effects. 



Reynolds numbers (R e ) used in various studies involving oscilla- 

 tory flow are not defined by convention, but rather in ways convenient 

 to the particular study; thus, no one definition is used consistently. 

 Dai and Kamel (1969) conducted model tests at three different scales. 

 A Reynolds number was defined using, for velocity, the water particle 

 velocity parallel to the side slope at a distance below SWL related to 

 the armor unit size. The length unit is the characteristic armor unit 

 diameter. The velocity is determined from empirical graphs, and is a 

 function of period, depth, and armor unit diameter. However, a separate 

 graph is apparently required for each wavelength and only one is given. 

 This R e is difficult to use as defined. 



Hudson and Davidson (1975) present data from Dai and Kamel (1969) 

 using a different Reynolds number for rubble-mound stability tests 

 defined as 



(gH D=0 ) 112 (kj.) 

 Re = " > (10) 



where 



g = gravitational value 



tip _q = zero- damage wave height 



k r = characteristic diameter -r, 



v = kinematic viscosity of water 



This latter definition is more "workable," but depends on the empirical 

 value of H^^. 



The implicit understanding when plotting data against R e must be 

 that the other required dimensionless terms have the same value in the 

 different scale models. Hudson and Davidson plot the stability number 

 versus R g , and the assumption in this case, then, would be that the 

 wave conditions are sufficiently specified by using the zero-damage wave 

 height and armor unit dimension. For the plot given by Hudson and 



104 



