extends to high rates of scour and high degrees of sand agitation. 

 Similarly, Figure 18 of Mogridge and Kamphuis (1972) is reproduced in 

 Figure 4 with lines of constant cj) added. Again, for small values 

 of (() , n/a is approximately constant, but, as (f) increases, n/a 

 decreases and its dependence upon a/D, increases, both relatively 

 rapidly. As (j> increases, n/a decreases more rapidly than does X/a, 

 so that the ripple steepness, n/A decreases. 



In Figure 5, X/D as function of 2a/D, from several studies, is 

 compared with the envelope curve of Mogridge and Kamphuis (1972) . 



2 /2a 



^ « Ki^) . o°i 



Examination of the sources of the plotted data reveals that the effect 

 of (J), or of X2, is seldom such as to displace the points significantly 

 from the envelope, so that displacements are to be interpreted as disa- 

 greement or as scatter. The studies included in Figure 5 are: 



(a) Bagnold (1946), using an oscillating tray in still 

 water and grains of quartz, coal, and steel. 



(b) Carstens, Neilson, and Altinbilek (1969), using an 

 oscillatory-flow water tunnel with quartz sand, flint shot, 

 and glass beads. 



(c) Yalin and Russell (1962), using a wave tank and grains 

 of quartz, coal, and Lucite. 



(d) Kennedy and Falcon (1965), using a wave tank and 

 grains of quartz (two sizes) and two plastics. 



(e) Inman and Bowen (1962) , using a wave tank and a 

 single quartz sand; also Inman (1957), observing in the field. 



(f) Dingier (1975) , using a wave tank and quartz sand 

 (two sizes) and observing in the field. 



Dingier (1975) discusses most of these studies and presents plots similar 

 to those in Figure 5. 



In general, for 2a/D < 2x10^, the data in Figure 5 agree with the 

 curves of Mogridge and Kamphuis (1972) as reduced to equation (9) or (10) . 

 An exception is the leveling off of the curves of Bagnold (1946) in 

 Figure 5(a). Since laboratory observations in Figure 5 for 2a/D < 2x10^ 

 include grains of quartz over a wide range of sizes, and grains of other 

 materials, they extend as well as confirm the results of Mogridge and 

 Kamphuis (1972) . 



20 



