Suggested Scaling Criteria Based on Fall Speed Parameter 



Previous Efforts 



34. Dalrymple and Thompson (1976) were among the first to propose movable-bed modeling criteria 

 that maintained similarity between prototype and model values of the fall speed parameter. Several sets of 

 scaling criteria were developed by Dalrymple and Thompson, and some were tested in the laboratory. 

 Among their more interesting findings were that the foreshore slope appeared to be independent of the 

 initial profile and that the experimental results were repeatable. One of the developed model laws required 

 an undistorted model with the waves scaled according to the Froude criterion and sand grain size selected 

 to preserve the prototype value of the fall speed parameter. This law was not tested in the laboratory, but 

 Dalrymple and Thompson stated that it appeared to be most practical because it also preserves the wave 

 steepness parameter. Additionally, they recommended the model bed material be sand to avoid possible 

 "alien" effects. 



35. Kamphuis (1982) concluded that preservation of the fall speed parameter eliminates most of the 

 scale effects associated with attempting to geometrically scale the grain size diameter of quartz sand. 



36. Vellinga (1982) presented distorted movable-bed modeling guidance for dune erosion that 

 incorporated sediment fall speed. Correct distortion in the model was determined through a scaling series 

 involving 24 small-scale tests with various combinations of three length scales and four sediment sizes along 

 with some prototype-scale laboratory experiments. Irregular wave trains were used during testing. These 

 model results were used to determine empirical exponents in the scale relationships. In considering the 

 undistorted version of Vellinga's scaling relationship, the guidance is equivalent to preserving the fall speed 

 parameter in an undistorted Froude model. 



37. Hughes (1983) also proposed a distorted model law for movable-bed models of dune erosion that 

 was derived specifically to preserve the fall speed parameter. Model distortion was achieved by modifying 

 the time scale from the Froude requirement so that trajectories of falling particles remained in similitude. 

 Although the scaling relationships diff'ered with that of Vellinga (1982), the undistorted versions of both 

 model laws were identical and conformed to that recommended by Dalrymple and Thompson (1976). 

 Discussions of the distorted model law were presented by Sayao (1984) and Vellinga (1984). Hughes (1984) 

 recommended the undistorted version of the model law be used when possible so that the wave steepness 

 would also be in similitude. 



38. Sayao and Guimaraes (1984) reviewed previous distortion relationships for movable-bed beach 

 profile models and tested four similarity criteria in a two-dimensional (2-D) wave tank. Their results 

 indicated an influence of the fall speed parameter relative to a critical value representing demarcation 

 between onshore transport and offshore transport. They recommended that it was necessary for both 



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