33 



The general expression for the law of sand transportation in the form 

 of sand ripples remains to be obtained. As it is assumed on the basis- 

 of table 2 that in the bar environment sand transportation is inde- 

 pendent of the position of sand ripples, the desired law can be 

 written immediately from equation 15 with the term AH /Hi omitted. 

 Accordingly, 



QrT __f ( I -ylgHidoM H doM • „ \ fiQX 



f^^2-j2 yPJVs> - ^^2' ^' h <T4>) (18) 



In the test under study the parameters on the right hand side are 

 constants and from the data for the test we obtain 



^=0.039 (19) 



The data used to establish the relation are: Qr= 1.21 pounds (weight) 

 per foot per hour, ^=1.4 seconds, Psfir=137 pounds (weight) per 

 cubic foot and ^i=0.58 foot. As an application to a natural con- 

 dition, let us suppose that Hi—Q feet, T=3 seconds and other condi- 

 tions are similar to those of the test. The rate of transportation 

 of sand would be: Q,=0.039X137X6X6/3, or 64 pounds per foot 

 width per hour. 



The problem of sand transportation in this form of ripples on sea- 

 beds is an important one and can be treated with sufficient detail only^ 

 by an independent investigation. The investigation should be made 

 for the bar environment, and for the seaward region adjacent to the bar 

 envu'onment. The law probably assumes different forms in the two 

 regions. 



C. Extreme water surface variations in the bar environment. — The bar 

 environment, as was mentioned previously, is limited seaward by 

 waves which are beginning to break and shoreward by waves which 

 reform following the breaker. Variations in the water surface eleva- 

 tions at these points determine the flow of energy into and out of the 

 bar environment. In studying breaking of waves, the first question to 

 consider is the determination of the locality where breaking is im- 

 pending. The upper curve in figure 18 shows the dependence of the 

 ratio AHi/Hi, upon the wave steepness, ao/\o- Here Hi is the depth of 

 water at the locality where the waves are beginning to break, and 

 A^i is the elevation of the crests at the point of impending wave 

 break, measured from the level of the undisturbed water. Thus, if 

 A^i is known the curve just given will enable us to evaluate Hi. 

 Obviously, AHi is a function of ag and flo^o in the form 



AHJao==yiaJ\o) (20) 



