The remaining observations, with two types of plastic beads 

 (p /p = 1.28, 1.05), give values of (})g somewhat higher, presumably 

 due to an effect of smaller Pg/p- In Manohar's (1955) experiments, 

 varied over the range, 14 < r < 356. The condition for sheet flow 

 observed by Chan, Baird,and Round (1972) is given by their equation 

 (iii) which can be written. 



<).s = 23.2 r-l/3(a/D)V3 . (13) 



In their experiments, using various fluids and granular materials, Pg/p 

 and r varied over the ranges, 1.04 < Pg/p < 5.1 and 0.16 < r < 160. 

 Based on observations on the seabed. Dingier (1975) concluded that the 

 ripple steepness r\/X begins a decline at (j) around 40 and that ripples 

 disappear at <^ around 240, or 



240 . (14) 



This value is not greatly larger than Carsten's (1966) earlier proposal 

 of around 169 (i.e., around 13^). 



f. Three-Dimensional Bed Forms . Several of the studies cited 

 above contain references to three-dimensional bed forms. Bagnold 

 (1946) discovered a small regular "brick pattern" when a was reduced 

 to about A/6. Manohar (1955) observed a similar pattern at "very short 

 strokes" as 03 increased "almost to the point of ripple disappearance." 

 Kennedy and Falcon (1965) also report brick patterns but at relatively 

 large periods and orbital diameters, with 2a/ A « 10. In contrast, 

 Carstens, Neilson, and Altinbilek (1969) describe three-dimensional bed 

 forms which, unlike the brick patterns, were irregular and were often 

 observed. They found that, with increasing a/D, two-dimensional ripples, 

 having attained maximum size at a/D = 775, gave way to three-dimensional 

 forms which persisted until their disappearance at a/D = 1,700. Inman 

 (1957) has defined the degree of two and three dimensionality in terms 

 of three categories which he includes with his observations. Outside 

 of Inman (1957) and Carstens, Neilson, and Altinbilek (1969) few 

 references to three-dimensional forms are found; therefore, it must be 

 presumed that the bed forms under discussion are two dimensional. 



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