the grains to unnatural [though possibly negligible) accelerations. 

 Stationary beds are provided by wave tanks and oscillatory-flow water 

 tunnels. Inman and Bowen (1962), Kennedy and Falcon (1965) and Yalin 

 and Russell (1962) used wave tanks. Although the mechanics of sand 

 movement by waves in tanks are that of the prototype, limitations in 

 tank size and wavelength keep wave periods rather small, typically less 

 than 3 seconds. Oscillatory-flow water tunnels may or may not be 

 limited in period. Carstens, Neilson, and Altinbilek (1969) used a 

 tunnel with a rather wide cross section well adapted to observe three- 

 dimensional bed forms but which was restricted to a single period of 

 oscillation (3.56 seconds). Mogridge and Kamphuis (1972) and Ranee 

 and Warren (1968) had the use of large tunnels without restriction on 

 period. The tunnel of Chan, Baird, and Round (1972) was limited in its 

 range of period and by a circular cross section only 5 centimeters in 

 diameter, but was suitable for use with fluids other than water. 

 Inman (1957) and, later. Dingier (1975) observed ripples on the seabed 

 itself. The seabed lacks all the usual laboratory restrictions of 

 size and scale, but it is out of the observer's control so that the 

 cause of an effect may be obscured. Both Inman (1957) and Dingier 

 (1975) discussed the problem of defining an amplitude and a frequency 

 for the bottom water motion for field conditions where the wave spectra 

 have many components. 



b. Initiation of Grain Motion . The first stage of ripple develop- 

 ment, the initiation of grain motion, has been the most studied. 

 Silvester (1974) provides references to 13 separate criteria, to which 

 may be added others of Komar and Miller (1973; 1975), Chan, Baird, and 

 Round (1972), Sternberg and Larsen (1975), and Dingier (1975). Of the 

 assembled criteria, 14 can be put in the dimensionless form, 



^^ = const. r"(^)^ . (6) 



This particular form of equation (3) is the usual result of fitting data, 

 over a limited range, with a straight line on a log-log plot. Some of 

 the criteria apply specifically to laminar or turbulent boundary layers. 

 Criteria which can be defined by the data of Bagnold (1946) and Manohar 

 (1955) have been discussed by Komar and Miller (1973). 



However, taken altogether, the available data do not clearly define 

 the function (t)^(a/D, r, p^/p). Among the 14 formulas represented in 

 equation (6), g varies between zero and 2/3, while a varies between 

 -2/5 and +38/45, leaving it open to question whether an increase in r 

 causes (|)c to decrease or increase. in contrast, the effects of a/D are 

 relatively clear and trends of the data of various observers are shown 

 in Figure 2 by plots of (|)(> as function of a/D. Included in the figure 

 are trends from the frequently cited Bagnold (1946) and Manohar (1955) 

 with three data points from Carstens, Neilson, and Altinbilek (1969). 

 To extend the range of r in the data, trends have been added from 



15 



