given set of values of the independent variables, 

 followed consists of the following seven steps. 



The procedure to be 



a. The necessary condition that has to be satisfied for the method 

 to be applicable is that the flow within the boundary layer caused by the 

 surface wave is unstable. To test whether or not this condition is satis- 

 fied in a particular case the graph in Figure 1 may be used. The roughness 

 size e can be taken equal to D while the velocity u is calculated from 



where 



H u , a H u 2 TT d 

 a = — cosech kd = — cosech 



2 2 \ 



The point with coordinates D and u / v is plotted in Figure 1 and accord- 

 ing to its position relative to the experimental curve for the three- 

 dimensional roughness , a prediction can be made about the character of 

 the flow in the boundary layer. 



b. Assuming that the test in step a proved that the condition of 

 instability is satisfied, we proceed with the determination of the flow 

 field in the boundary layer. It has been shown in section 3 that the mean 

 unsteady velocity in the layer is given by the expression 



j"l + f 2 2 (y) - 2fi(y) cos f 2 (y) Tsin(ujt + 9) 



where 



-1 fl(y) sinfa (y) 



= tan 



l-fl(y) cosf 2 (y) 



It was also shown that 



_ 133 y 



f 1 ( y ) = .5 e ag D 

 2/3 



and 



where & = Jt 



c The value of the parameter I f| is next calculated from equation 

 (4-10} ; i.e. 



Ps " Pf gD 



K| = Pf | u|a 



The velocity u is measured at a distance 0.35D from the theoretical bed, 

 which means that 45.55 



and 



fl(y) = .5 e 



*2(y) = -25 cpD) 



a3 

 2/3 



25 



