Selected Scaling Criteria 



53. The selected scaling guidance consists of simultaneously satisfying two scaling criteria in an 

 undistorted movable-bed model. The first is the well-known Froude criterion for the hydrodynamics that 

 arises if the ratio of inertial forces to gravity forces is held constant between prototype and model. The 

 FVoude criterion results in the relationship 



Nt = ^/Wt, (2) 



where N represents the prototype-to-model ratio of the subscribed parameter, t is time, and i is length. 

 Note that scale ratios defined in this manner are usually greater than one and are always dimensionless. In 

 deriving Equation 2, the gravity scale, Ng, was set equal to unity. 



54. The second criterion requires maintaining similarity of the fall speed parameter between prototype 

 and model, i.e., 



WpTp WmTm 



where the subscripts p and m represent prototype and model, respectively. Rearranging Equation 3 yields 



Hf_^Wp_Tp_ ^^^ 



Hm Wm Tm 



Equation 4 can be written in terms of scale ratios as 



Nh = N^Nt (5) 



55. Recognizing in an undistorted model that Nh = Ni and that the wave period will scale the same 

 as the hydrodynamic time scale, the combination of Equations 2 and 5 results in the unique scaling 

 relationships satisfying both criteria: 



Nt=N^ = \/Ni (6) 



Comparison to Xie's Scaling Guidance 



56. As mentioned, various parameters other than the fall speed parameter have been suggested for use 

 in characterizing sediment transport processes. It is instructive to examine one of these parameters in more 

 detail because it was found useful for analyzing some of the scale model results arising from this study. 



57. Xie (1981, 1985) conducted numerous small-scale movable-bed model tests to examine the scouring 

 of bed material adjacent to a vertical seawall subjected to nonbreaking waves. He observed two distinctly 

 different responses in bed form that appeared to correspond to different mechanisms of sediment transport. 



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