d. With | Y| known the curve through the experimental points in 

 Figure 8 can be used to obtain $. This curve is very closely approximated 

 by the graphical representation of" the equation 



COS 3 F 



e. The oscillatory sediment transport rate qg in the bed layer 

 which we may call the "oscillatory bed-load rate" is calculated from f 

 through equation (4-26), i.e., 



Y s V S(p s -P f ; 



p f D -3/2 



f . The concentration c of the solid particles that at any time 

 happen to be in a state of motion within the bed layer (of thickness 2D) 

 is 



c„ = .618 



2D (u B ) 

 where Ug is the value of u from (3-24) at y = D. 



g. The rate of sediment transport per unit width in the direction 

 of any incidental secondary flow described by U(y) will be 



p2D 



% = c o ! u(y) d v 



In the general case U(y) is an additional independent variable which has 

 to be determined by methods similar to the ones used in the determination 

 of the surface wave characteristics. In the absence, however, of any such 

 flow the only possible steady mean motion in the boundary layer is due 

 to the surface wave itself which is called the "second-order drift flow". 

 This steady flow within the boundary layer is in the direction of the wave 

 propagation. The expression describing the velocity distribution associ- 

 ated with this flow is of the form 



- a 2 ouk f -Ry Q -2f 

 u = o — k Si a 1 5_8 e cosgy+3 e 

 2 sinrkd [ 



as proposed by Longuet-Higgins . This expression can be substituted for 

 U(y) in the above integral to calculate Qg. This is the sought-for value 

 of the rate of transport of bed material in the direction of the wave 

 propagation. 



9 . DISCUSSION OF THE RESULTS 



The procedure outlined in the preceding section leads to a quantita- 

 tive answer of our problem. In trying to apply the method to an actual 



26 



