their dependence on orientation and exposure to the flow, makes such a 

 study infeasible. Also, a distinction must be made between setting sand 

 in motion at points on a relict bed form and establishing a new bed form. 

 A new oscillatory flow may at first move sand on sharp relict ripple 

 crests, but such flow may merely round the crests until the sand ceases 

 to move. In predicting stable bed forms, it is more pertinent to deter- 

 mine the minimum conditions of flow required to sustain them, assuming 

 that any stimuli which may be needed to initiate their development will 

 always be present. Minimum conditions to sustain a rippled bed can 

 reasonably be sought in terms of a minimum value of (j) . Lofquist (1975) 

 found that an oscillatory flow, combined with an effect of permeability, 

 became unable to sustain ripple migration at a value of tf) around one- 

 fourth (|)j,. Carstens, Neilson, and Altinbilek (1969), for a/D = 139 

 (in their experiment 62), identified a minimum 4> = 2.15 needed to 

 continue the growth and spread of small ripples initiated by a foreign 

 object. A reduced <p could possibly have maintained the ripples in 

 equilibrium after they had attained full size. 



It was found that the conditions required to initiate grain motion 

 on a leveled bed in these experiments were also sufficient to initiate 

 vortex ripples, though, for the finer sands, these ripples always 

 started at some point at the ends of the test bed. However, it 

 appeared that if the test bed were boundless the criteria for grain 

 motion and ripple formation would indeed be distinct. The difference 

 between i^j. and cj)^ appears to be small, negligible for coarse sand, but 

 increasing as the grain size (r) decreases. 



In these experiments, the rolling-grain ripples of Bagnold (1946), 

 were observed with the 0.18- and 0.21-millimeter sands but not with 

 the 0.55-millimeter sand. Such an unpredictable occurrence is 

 characteristic of previous observations. Despite their persistence, 

 these ripples appeared to play no part in the development of vortex 

 ripples. This passive behavior contrasts with the more active role 

 described by Bagnold (1946), Manohar (1955), and Carstens, Neilson, and 

 Altinbilek (1969), and suggests that rolling-grain ripples are not an 

 essential part of ripple development. 



2. Growth of Ripples . 



The profiles were always initially two dimensional when the ripples 

 were small, but during the subsequent period of rapid growth they became j 

 in varying degree, three dimensional. Following this period, as the 

 profiles approached equilibrium, the ripples either became again two 

 dimensional or remained more or less three dimensional. 



The dimensionless initial ripple length, X^/D, was found to be 

 approximately constant for each sand, to increase moderately as r 

 decreased, and to be independent of a/D. That X^ is independent of a 



73 



