while the rate of removal of grains from the bed is a function of the 

 local flow intensity. The functional relationship between the "bed-load 

 rate" in a stream and the flow intensity constitutes the "bed-load function" 

 while the equation expressing this relationship is defined as the "bed- 

 load equation". With the help of this equation it is possible to calcu- 

 late the bed-load rate for given flow conditions and bed composition. 

 Finally, the concentration in the bed layer which can be easily calculated 

 from the bed-load rate is assumed to be equal to the concentration of the 

 suspension load at the reference level. This helps to find the complete 

 solution to the problem which expresses the total rate of transport as the 

 summation of the suspension rate and the bed-load rate. The significance 

 of the concepts of the bed layer, the bed-load function and the bed-load 

 equation is evident. In the absence of substantial evidence to the con- 

 trary it is legitimate to assume that similar concepts hold true in the 

 case of an oscillatory mean flow. Accepting a priori the existence of a 

 bed layer and of a bed-load function, our objective will be to develop 

 the bed-load equation associated with this type of flow. In our effort 

 along this line the valuable experience from the steady mean flow will be 

 used as a guide. The procedure leading to the derivation of the bed-load 

 equation will be described in the following section. 



b. The Bed-load Equation 



It is a well-established fact that the distortion of the flow field 

 around a solid particle resting on the bed of a stream generates a lift 

 force acting on the particle, even if the latter is well-sheltered within 

 the sublayer. Naturally the larger the size of the particle relative to 

 the thickness of the undisturbed laminar sublayer, the more pronounced is 

 the distortion and the greater the intensity of the lift force. This 

 force will tend to dislocate the particle and move it away from the solid 

 bed. As long, though, as the particle is still in contact with the bed, 

 the lift force is acting only vertically upwards and it can be expressed 



2 . 

 L = C L p f \ A 2 D (4-4) 



Cl is the coefficient of lift, A a shape factor and u the instantaneous 

 velocity acting at a distance y from the theoretical bed. In the case 

 of a steady mean stream the location of the theoretical bed and the level 

 y relative to it at which the velocity must be taken have been established 

 experimentally by Einstein and El-Samni (1949). They conducted flume ex- 

 periments with plastic spherical balls 0.225 feet in diameter placed in a 

 steady stream of water. The theoretical bed has been determined as the 

 reference level from which distances should be taken so that the measured 

 values of the mean velocity would give the best fit to a logarithmic 

 distribution. It has been found that the matching of this profile was 

 the most satisfactory when the theoretical bed was taken at a distance 

 0.20 D below the top of the spherical particle. The distance y at which 

 the velocity should be measured in calculating the lift force has been 



