force necessary to produce incipient motion. However, model scales 

 based on the principles of unidirectional motion may not be strictly 

 applicable to the case of oscillatory wave motion, but a first approxi- 

 mation is probably permissible. By setting a lower limit to the model 

 Reynolds number and computing the prototype Reynolds number, the ratio 

 of the prototype-to-model Reynolds number will determine the scale of 

 the characteristic length used in the vertical direction of the model. 

 In this procedure, it is assumed that the ratio of model-to-prototype 

 velocity is a function only of the depth ratio, as determined by the 

 Froude law. 



If the model sediment material has not been selected beforehand, a 

 revised approach can be developed (Gessler, 1971). To have similarity 

 in incipient motion and bedload transport, the bed mobility in the model 

 and prototype should be the same at homologous points. This mobility is 

 determined by the ratio of the actual Shields parameter to the critical 

 Shields parameter. The reason for this modification in approach is that 

 the critical Shields parameter depends somewhat on the grain Reynolds 

 number for values below about 150. For ordinary model materials (fine- 

 grained sands), the grain Reynolds number is on the order of 5 to 10. 

 The Shields diagram is poorly verified in this range, so the grain 

 Reynolds number should not be smaller than about 15. This can be 

 achieved by using a coarser bed material in the model than in the pro- 

 totype but one that is less dense. The Shields parameter is 



7 dS 



"^"^ (7-9) 



(T, - 7w)D<, 



where S is the channel slope and Dg the particle size. By using 

 this definition and evaluating the ratio of the prototype-to-model 

 Shields parameters, a generalized criterion will evolve which can be 

 solved for the specific weight (submerged) of the bed material to be 

 used in the model. (The reason for using a lightweight material refers 

 to the idea that the grain size is relatively too large in the model.) 

 The final selection of the model material will depend on the materials 

 available; however, a slight adjustment in the desired grain size may 

 be necessary. 



The analyses of Gessler (1971) are applicable only to unidirectional 

 flow at one specific discharge; this means that highly unsteady flow pro- 

 cesses like surface gravity waves cannot adequately be modeled by this 

 process. Changes in discharge require that the time scale of the dis- 

 charges be modeled according to the time scale associated with the sedi- 

 mentation processes to obtain similarity in bed-forming processes. The 

 considerable discrepancy between the hydrodynamic and sedimentological 

 time scales means that the sedimentation processes are advancing too 

 rapidly in the model. Gessler concludes that no matter how carefully 

 the design is done, it remains absolutely essential for distorted-scale 

 as well as undistorted-scale models to be verified against field data. 



474 



