the data, which were obtained mostly in exposed coastal waters. However, 

 there appears to be some tendency for longer crested ripples to associ- 

 ate with larger values of <j) and a/D. Of the 5 observations for 4) < 4, 

 none is long crested; of the 27 observations for (j) > 46, none is short 

 crested, and all of the 4 observations for (f) > 110 are long crested. Also 

 five observations for conditions of limited fetch, with T < 3.5 seconds, 

 form a separate group displaced, at given tf), toward smaller a/D. These 

 are all long-crested ripples. Inman (1957) found a strong tendency for 

 long-crested ripples to occur nearshore in shallow water, which would 

 imply an association with larger values of (f). However, the effect of 

 depth appears so strong as to suggest some factor beside ((), such as 

 the increasingly two-dimensional character of surface waves as they 

 advance over a shoaling bottom. 



VII. INTERPRETATION OF RESULTS 



1. Initiation of Grain Motion and Ripple Formation . 



The observations of the initiation of grain motion on a flat bed 

 in these experiments have provided values of (t)^ as functions of a/D and 

 r, as in equation (3) . These data, and a separate curve for each 

 value of D, or of r, are shown in Figure 12. It is seen that to 

 suppress the effects of r and to approximate all the data with a 

 single straight line on the logarithmic plot would introduce new scatter. 

 Approximations of this sort certainly account for a part of the large 

 disparity between trends in the data compiled by different observers, 

 as indicated inFigure 2. However, the major part remains attributable 

 to the subjective element usually involved in determining (j)(., as discussed 

 in Section 111,1. This element can account for the present values of (jj^ 

 plotting somewhat above the composite curve in Figures 2 and 12. The 

 effects of surface compression, investigated in two experiments, do not 

 appear very significant. 



The applicability of a Shields criterion was tested with the obser- 

 vations in this study. Application of the criterion involves a computa- 

 tion of the oscillatory bottom stress which remains somewhat uncertain. 

 Although the successful use of a Shields criterion does provide insight 

 into the mechanics of incipient motion, the prediction of incipient 

 motion can be approached directly, and perhaps more easily, by the 

 empirical determination of (^(. as a function of a/D and r. 



Carstens (1966) has stated that the concept of incipient grain 

 motion on a flat bed is of doubtful relevance in the formation of 

 ripples, since the seabed is seldom flat, and he would suggest a study 

 of the minimum conditions for the stimulation of ripples by foreign 

 objects and it may be added here, by relict bed forms. However, the 

 innumerability of foreign objects able to stimulate ripples, including 



72 



