He classified Type I scour as fine bed material moving largely by suspension so that scouring occurs at the 

 nodes of the regular standing waves and deposition occurs about the antinodes. Type II scour occurs when 

 coarse-grained material moves as bed load, scouring sediment halfway between the nodes and the antinodes 

 and depositing at the nodes of the standing wave pattern. After testing several parameters, including the 

 fall speed parameter, Xie presented a criterion for distinguishing between the two scour patterns that 

 depends on the grain size of the bed material and on the wave conditions. The criterion is based on the 

 parameter 



w 

 where 



Umax = horizontal component of the maximum orbital water particle velocity near the bed 



Ut — critical velocity for incipient motion of the sediment 



w = sediment fall speed 



This parameter gives a relative comparison between the horizontal water particle speed beyond that 

 necessary for incipient motion and the speed at which the sand grain settles. High values of the parameter 

 imply movement by suspension (turbulence-dominated), and low values correspond to bed-load-dominant 

 conditions. A similar parameter was proposed by Le Mehaute (1970), who stated that kinematic similarity 

 was important for modeling beach profiles at small scale and suggested that the ratio of the horizontal 

 component of the orbital water velocity to the sediment fall speed be maintained. 



58. Xie (1981) suggested that similarity of the parameter given by Equation 7 should be maintained 

 between prototype and model, but noted that this would be difficult at times because of the dependence of 

 both Ut and w on grain size. Barring complete similarity, he recommended that both prototype and model 

 at least be in the same range for the type of scour being modeled, i.e., keep the value of the parameter 

 above 17 for Type I scour of fine sediment and below 16 for Type II scour of relatively coarse sediments. A 

 strong correspondence between the fall speed parameter and Xie's parameter is evident and prompts 

 further investigation. 



59. The scaling criterion derived from maintaining similarity of Xie's parameter in an undistorted 

 Froude model is developed as follows: 



'Umax-UA fUma.-U,^ 



(8) 



where once again subscripts p and m represent prototype and model, respectively. Rearranging Equation 8 

 yields 



(-^), 



{U,na.\ 



22 



