Although a three-dimensional character of the bed form might be 

 initiated and then conditioned by the presence of channel walls, such 

 constraints are by no means its only possible source. This is shown 

 by the three-dimensional ripples observed by Inman (1957) on the 

 unbounded seabed. A likely source here are the lateral perturbations 

 in the flow over the bottom which must be found under surface waves 

 which are themselves not two dimensional. This supposition is consis- 

 tent with the irregular occurrence of long-, medium-, and short-crested 

 ripples (Fig. 30). It is further supported by the observed tendencies 

 for long-crested ripples to occur in shallow water under shoaling waves 

 and in protected areas where the fetch is short--both conditions likely 

 to favor more regular and two-dimensional surface waves. However, the 

 observations at short fetch are also at smaller values of a/D. It has 

 already been noted that oscillatory ripples should become more like 

 steady-flow ripples as a and T become large. Raudkivi (1976; pp. 

 62-65) describes steady-flow ripples as typically three dimensional. 

 These considerations are consistent with a tendency for oscillatory 

 ripples to become more three dimensional with increasing a/D. 



5. Disappearance of Ripples . 



To forestall damage to the screens (Table A-2, experiment 67) in 

 these experiments, (f) had to be limited to values xmable to produce 

 sheet flow. Therefore, this section only discusses the criteria of 

 Manohar (1955), Chan, Baird, and Round C1972), and Dingier (1975), 

 given by equations (12), (13), and (14), respectively. In equations 

 (12) and (13), (j)s depends on both a/D and r; in equation (14) this 

 dependence is absent, perhaps due to relatively small ranges of a/D 

 and r in Dingier 's (1975) observations of sheet flow, with a/D 

 between 5x10^ and 10*^ and with D between 0.128 and 0.158 millimeters, 

 corresponding to r ^5.8 and 8.0. Curves of ()) = (jj^, given by equations 

 (12) and (13) for r = 5, 10 and by equation (14), are plotted against 

 a/D in Figure 32 (discussed in Sec. VII, 6). The curves in Figure 32 are 

 solid where supported by observations and dashed where extrapolated. 

 In the region of Dingier 's (1975) observations of sheet flow, the 

 criteria are in remarkable agreement, considering their diverse 

 derivations and the distortions to which equations (12) and (13) are 

 ostensibly subject. Unnatural accelerations of the oscillating tray 

 may have reduced the (^c, observed by Manohar (1955) , especially at 

 smaller values of a/D. Effects of confinement in the pipe test section 

 of Chan, Baird, and Round (1972) are clearly severe on bed forms with 

 height comparable to the pipe diameter (5.1 centimeters), but may have 

 lessened as the bed flattened to approach sheet flow. (However, in 

 experiment 55 cj) exceeded (jig by eq. 13 without attaining sheet flow.) 

 Taken together, equations (12), (13), and (14) suggest a (^^ as a modifica- 

 tion of equation (14) to allow for relatively slight effects of a/D and 

 r. These effects are not yet established, but ^^ appears to increase 

 with increasing a/D and, usually, with decreasing r, though perhaps not 

 always, as suggested by the crossing extrapolations of equation (12) 

 for r = 5 and 10. 



78 



