smaller and larger U. With D = 0.18 millimeters, this line can also 

 be defined as a/D = (222 sec~-^)T, or as ^ = 21.3. The first defini- 

 tion confirms the observation of Carstens, Neilson, and Altinbilek 

 (1969) that bed forms are two or three dimensional as a/D is less than 

 or greater than 775, when T = 3.56 seconds (the period in their experi- 

 ments), but conflicts with their criterion as stated in terms of a/D 

 alone. The second definition conforms generally, though only roughly, 

 with Carsten's (1966) earlier criterion that two- and three-dimensional 

 forms occur as c})^ is less than or greater than approximately 6.5. 



In Figure 28, with the 0.21-millimeter sand, a line of constant (() 

 again appears to separate two- and three-dimensional regions for 

 moderate and large values of a, but it cannot be extended to small 

 values of a, where a two-dimensional character seems dominant at all 

 values of T. In this case, for small values of a/D, the criterion of 

 Carstens, Neilson, and Altinbilek (1969) seems to apply. A curve 

 separating two- and three-dimensional regions has been attempted in 

 Figure 28, but its contorted character warns of uncertainty. Wliy, at 

 small values of a, two- dimensional bed forms should occur at small 

 values of T with the 0.21-millimeter sand and not with the 0.18- 

 millimeter sand is difficult to say. It can only be suggested that 

 the relatively broad grain-size distribution of the 0.21 -millimeter 

 sand (Fig. 7) makes the dependence of bed form upon grain size less 

 precise, and that the larger grains act to place the 0.21-millimeter 

 sand in an unstable transition zone between the 0.18- and 0.55-millimeter 

 sands. For the 0.55-millimeter sand, all final bed forms were two 

 dimensional . 



Photos of final bed forms in four experiments with the 0.18- 

 millimeter sand are shown in Figure 29. The experiments have been 

 selected in two widely separated pairs at large and small values of 

 a (at N = 100,25). Each pair straddles the line of constant ^ which 

 separates the regions of two- and three-dimensional bed forms in Figure 

 27. The photos show that in each case the character of the bed form 

 confirms the choice of the symbol plotted in Figure 27 and that the line 

 of separation splits each pair. 



3. Results with Inman's (1957) Sea Floor Data. 



An attempt was made to establish conditions for the occurrence 

 of two- and three-dimensional ripples on the sea floor based on the 

 observations and definitions of Inman (1957) . As mentioned earlier, 

 he defined the ripple pattern according to whether the length of the 

 ripple crests was greater than 8X (long-crested), between 3A and 8A, 

 or less than 3A (short-crested) . Symbols for these patterns have been 

 plotted by values of a/D and cj) which, for 95 observations, could be 

 obtained from the data in Inman's tables (see Fig. 30). In general, the 

 three patterns are found to be mixed together over the (a/D,(j)) field of 



69 



