When studying problems of scour and deposition, it becomes necessary 

 to add the critical shear stress and sublayer criteria to the gravity and 

 frictional criteria, as developed by Graf (1971) . Introducing the empiri- 

 cal relationship between the bed particle diameter and Manning's n value 

 produces : 



where d is the bed particle diameter and R the hydraulic radius. When 

 model and prototype fluids are identical, four independent variables are 

 found, and three equations provide a solution. The problem is determined 

 if one of the four parameters is chosen, and the remaining three variables 

 are found from the equation solutions. A distorted-scale model was assumed 

 in this analysis. Various researchers have stated that some model laws can 

 be relaxed with little harm to the overall investigation. Einstein (1954) 

 suggested that the friction criterion, the Froude criterion, or the sub- 

 layer criterion might absorb further distortions. Under certain circum- 

 stances, small deviations from the exact similarity may be allowed, making 

 it possible to arbitrarily select more than one single variable. 



From the application to strictly coastal sediment modeling problems, 

 Migniot, Orgeron, and Biesel (1975) have stated that, since all of the 

 similitude conditions involved cannot be satisfied, the model scales, the 

 material size and density, and the current exaggeration cannot be deter- 

 mined by straightforward computations but must be chosen to obtain the 

 most favorable balance between all relevant phenomena. In many respects, 

 this is more an art than a science, and a feeling of the problem, previous 

 experience, and a perspective of the relative importance of each factor is 

 of paramount value. The sedimentological time scale can be derived from 

 general transport formulas, and when sand is simulated with a lightweight 

 material such as plastic with a density of 1.4, the sedimentological time 

 scale will be in the range of 1:1,000; this means that a year will corre- 

 spond to some 8 hours of model time. Although it is disquieting to note 

 that so much empirism prevails in the design of coastal movable-bed models, 

 the model is only fit for predictive use when it has successfully repro- 

 duced past evolution. While the various similitude conditions may not all 

 be satisfied, the conditions do not differ too much from each other, so 

 fairly satisfactory compromises can usually be found. For instance, model 

 material density required to satisfy these various prototype conditions 

 may typically vary from 1.3 to 1.6, while size exaggeration may vary from 

 1.0 to 1.7. 



The movable-bed coastal model by Kamphuis (1975) is a wave model in- 

 corporating coupled wave motion and sediment motion relationships which 

 have been determined experimentally. The unidirectional flow phase is 

 then added to the basic wave model and adjusted to yield correct results 

 for different situations. This is a basically different philosophy from 

 Le Mehaute (1970) who assumed that a coastal movable-bed model is a uni- 

 directional flow model modified by waves. The difference in scale laws 

 is quite evident when the results of their methods are compared. 



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