model and prototype values to be in the same range (either above or below the critical value), but did not 

 require similarity of the fall speed parameter between prototype and model. However, they recommend 

 that further tests using fine-grain sediment be undertaken to evaluate the influence of the fall speed 

 parameter. Tests conducted using lightweight cellulose acetate were not successful, and they recommended 

 avoiding these types of model sediments for beach profile modeling. 



39. Dean (1985) reviewed previous movable-bed modeling criteria and considered the dominant 

 physical mechanisms involved in surf zone sediment transport. He argued that the Shield's criterion need 

 not be met in the surf zone because turbulence, not bed shear, is the dominant cause of sediment 

 mobilization; and therefore, bed shear is not an important consideration above Reynold's numbers 

 constituting the fully rough range. Dean made specific recommendations for successful modeling of surf 

 zone processes: 



a. Undistorted model (equal horizontal and vertical length scales). 



b. Hydrodynamics scaled according to Froude similarity. 



c. Similarity of the fall speed parameter between prototype and model. 



d. Model is large enough to preclude significant viscous, surface tension, and cohesive sediment 

 effects so that the character of the wave breaking is properly simulated. 



40. Dean (1985) argued that, in an undistorted model, the fall trajectory of a suspended particle must 

 be geometrically similar to the equivalent prototype trajectory and fall with a time proportional to the 

 prototype fall time. This is accomplished by ensuring similarity of the fall speed parameter between the 

 prototype and the undistorted model. Dean noted that similarity of sediment fall trajectory could also be 

 achieved in distorted models, but he did not recommend distorting movable-bed models because of 

 uncertainties involved if sediment fall speed is not scaled according to the Froude criterion. An additional 

 concern is the possibility of dissimilar hydrodynamic surf zone conditions between prototype and model 

 when distorted scaling is introduced. Dean evaluated his recommendations with intuitive reasoning and by 

 examination of past results in light of the suggested criteria. He concluded by stating, "More extensive 

 data are required to establish further the degree of validity of the proposed modeling criteria." 



41. Vellinga (1986) thoroughly detailed his own work and the work of others in the areas of dune 

 erosion and movable-bed scale modeling. He examined many of the suggested parameters for characterizing 

 surf zone processes, and he reviewed various methods for developing potential scaling guidelines. 

 Large-scale model tests, with irregular waves having 2-m significant heights, were used to verify the 

 previously developed (Vellinga 1982) scaling criteria. The distorted model scaling criteria were tested in a 

 three-dimensional (3-D) situation having vertical scale of 60 and horizontal scale of 120 over straight depth 

 contours. Results confirmed the 2-D development within acceptable limits (Vellinga 1986). Small-scale, 

 2-D undistorted tests with Froude scaling of the hydrodynamics compared very well with large-scale tests 

 having the same value of fall speed parameter, showing geometrically similar profile development. Vellinga 



17 



