provides insight into the mechanics of ripple initiation, and suggests 

 the involvement of stress and the distances grains move over the flat 

 bed, rather than the action of a disturbance in the water, which would 

 move with amplitude a. However, Carstens and Neilson (1967) mention 

 vortices in the water just over the bed and perpendicular to the flow, 

 apparently, before ripples appear. Also, Folk (1976), cites many- 

 examples to show that bed forms are the result, rather than the cause, 

 of vortices in the flow. 



Observations of growing ripples suggest that n/a and A/a depend 

 primarily on (D/a)n, where n is the number of cycles since the 

 ripples first appeared. These (D/a)n observations are restricted to 

 the condition that U/U w 1 and, except for three experiments, to the 

 use of the 0.55-millimeter sand. The maturity of ripple profiles has 

 been found to depend on (D/a)n, involving an interval of time propor- 

 tional to (a/D)T. The period of rapid, and partly three-dimensional, 

 ripple growth may have been lengthened by the presence of tte channel 

 walls. On an unbounded bed, the development of a partly three- 

 dimensional bed form might be hastened by lateral spreading of more 

 nearly stable forms from wherever they occur. 



3. Size and Shape of Stable Ripples . 



Observations of X/D (Fig. 21) and of X/a and n/a (Figs. 22 and 23) 

 in this study are in general agreement with most of the previous studies 

 summarized in Figure 5. Despite minor differences, the observations have 

 confirmed the results of Mogridge and Kamphuis (1972), and extended them 

 to sands of different sizes at large a and T. The observations have 

 thereby supported the validity of the approximate equation (9) which 

 states that X is proportional to a, and that, with a held constant, 

 X is relatively insensitive to changes in T and to the associated 

 changes in U. These remarkable results deserve further study and 

 explanation. 



Occasional failures of laboratory observations to follow the curves 

 of Mogridge and Kamphuis (1972) in Figure 5 might be explained as the 

 effects of boundaries, by failure to achieve a steady state, or, possibly, 

 as distortions associated with oscillating trays. However, field and some 

 laboratory observations of X/D follow a trend below and away from these 

 curves as a/D increases to large values. This trend was discussed in 

 Section I,3,d and was identified with fine sands. It was then suggested 

 that the plots of Mogridge and Kamphuis (1972) might require modification 

 for smaller values of r. 



Whatever the effects of r, observed values of X/D should fall 

 progressively below the curves of Mogridge and Kamphuis (1972) as a/D 

 increases to large values. Continued adherence to equation (10) would 

 produce comparably large values of X/D. As a becomes infinite, the 

 oscillatory ripples cannot grow to infinite size but rather must turn 



74 



