We have shown already that q B can be determined for a given set of con- 

 ditions. In the following section a method will be described by means 

 of which c could be calculated from known values of q B . 



6. DETERMINATION OF c Q 



The rate of flow through a cross section of unit width and height 



h = 2D is 



2D 



q = [ U(y)dy (6-1) 



B 



while the rate of sediment transport through the same section at any 

 instance is 



,2D 



% 



U(y)dy (6-2) 



c is a measure of the concentration of the sediment which at any time is 

 at a state of motion within the bed layer. In this layer the rate of trans- 

 port due to the oscillatory flow is by definition equal to q B . Therefore 

 in a way similar to (6-2) we can write 



^2D 



u dy (6-3) 



^o 



The integral -^- i „ dy is nothing else but the expression for the mean 



Jo 

 value of u which we will denote by u m . We can write then 



q B q B 



P2D_ 2Du m (6 " 4) 



Jo " dy 

 u is obtained from equation (3-24) and naturally is a function of both 

 y and t. Hence the expression for the mean value will be of the form 



,2tt r.2D 



u(y,t)dydu)t (6-5) 



Um = 4 tt D J q 

 The calculation of u ra from (6-5) is a lengthy and tedious operation which 



has to be performed in each particular case. This renders the method 

 proposed here practically inapplicable. 



A simpler approach could be based on the assumption that u m is pro- 

 portional to the amplitude of the velocity at some arbitrary distance 

 from the wall within the bed-layer. In other words we postulate that 



u m = A 5 I " B I (6_6) 



21 



