29 



Figure 16 is plotted in accordance with the latter equation from 

 figure 15. The product psQ, being the specific weight of sand, is taken 

 to equal 137 pounds (weight) per cubic foot. The quantities Q and 

 AH are read from the curves in figure 15. Since Q was expressed as 

 pounds (weight) per foot width per hour and T is given in seconds, the 

 numerical value of QT involves the ratios of two different units of time. 

 Interpretation of the curve reveals that the rate of sand transportation 

 in the bar environment is controlled, among other things, by the total 

 displacement of the water surface, AH and that there is a critical dis- 

 placement value below which no appreciable transportation of sand is 

 possible. 



Further conclusions cannot be drawn on the basis of the meager 

 data available, but the problem is important enough to warrant a 

 separate and a more complete study. In an extended study the 

 effects of all the parameters entering into the right hand side of equa- 

 tion 14, should be examined. 



B. Sand transportation and sand ripples. — The discussion of sand 

 transportation given above refers to the initial conditions when the 

 beach is smooth and the slope of the surface is constant. Certain 

 changes in the beach surface occur as transportation continues. See 

 figure 14. Sand accumulates in the process of bar development and 

 sand ripples appear seaward of the bar. The effects of these two 

 changes are quite significant. With the formation of the bar the 

 breaker characteristics are changed, the total displacement of water 

 surface in the area between the breaker and the pomt of impending 

 break of the waves becoming nearly constant everywhere in this area. 

 The sand ripples signify a new mode of sand movement and a very 

 considerable reduction in the rate of sand transport, as will be shown. 



Sand ripples begin to form in the area just under the breaking wave, 

 apparently from two causes. One is the secondary undulations, which 

 manifest themselves at the surface of the breaker and are transmitted 

 to the bottom to form corrugations. The other is an accidental 

 unevenness of the bottom surface due to nonuniformity of resistance 

 of the sand or some other discontinuity of the bottom geometry. 

 Once the sand ripples have been started, in one way or another, a 

 continuous series of them results under favorable conditions. Their 

 final dimensions are controlled by the depth of water, the period of 

 the waves, the total displacement of the water surface during the 

 passage of waves, and the size and dispersion coefficient of the sand. 



Movement of sand in the bar environment after sand ripples have 

 covered the entire beach surface appears to take place in the following 

 manner. At the instant that a crest is moving over a sand ripple, the 

 motion of water particles just above the ripple is toward the shore. 

 At this moment the sand of the ripple surface is moved toward the 



