This study was conducted to further refine Noda's (1972) empirical 

 scale-model relationship and evaluate the validity and applicability 

 of that model law. The study plan consisted of three parts: 



(a) Investigation of the effects of sediment-size distribution on 

 scale models; 



(b) investigation of the effects of sediment shape on scale models; 

 and 



(c) experiments by Tetra Tech, Incorporated, and evaluation by CERC 

 of the validity of the proposed scale-model law. 



II. REVIEW OF LITERATURE ON EQUILIBRIUM PROFILES AND BEACH MODELING LAWS 



1. Hydrodynamic Conditions . 



Fan and LeMehaute [1969) and Noda (1971) reviewed in detail the 

 hydrodynamic conditions required for theoretical similitude and reduced 

 those conditions to the equations presented below. The term nquantity 

 denotes the ratio of model to prototype with the subscript indicating 

 the parameter being modeled and X and y are the horizontal and 

 vertical scales, respectively. 



a. Condition 1 . Coastal fluid phenomena are generally dominated by 

 gravitational and inertial forces and hence the Froude number F is an 

 important parameter: 



Ci) 



(gd)^'^ 



The requirement that np = 1 yields: 



a/2 



UtI \ dr, / 



where subscripts m and p refer to model and prototype values respectively, 

 and thus : 



1/2 c^^ 



n^ = y ' . (3) 



A major parameter affecting beach profiles is the deepwater wave steepness, 



Ho/Lo; if this parameter is to be preserved in model and prototype, then 



the wavelength must be proportioned like the vertical scale and consequently. 



n = y . (4) 



