However, the horizontal components of the resultant forces are larger 

 at the smallest bottom clearances, even though the lift phenomenon is 

 absent. The presence of the bottom boundary produces an asymmetric flow 

 field around the pipeline. The resulting velocities and accelerations of 

 the water particles over the pipe section are thus modified by the presence 

 of the boundary, and the associated horizontal forces are larger than they 

 would be if subject to the same kinematics in the absence of the boundary. 

 Tlie increased horizontal forces on pipelines located close to the bottom 

 are reflected in increased values of the coefficients of mass and drag, 

 C^ and Cq. 



2. Orientation Angle Considerations. 



The coefficient of lift calculated in the least squares analysis of 

 the experimental data was computed using two alternative approaches 

 (Fig. 38) : (a) the total horizontal water particle velocity in the 

 direction of wave advance, with the projected area of the pipeline in the 

 plane perpendicular to the direction of wave advance; and (b) only the 

 component of the horizontal water particle velocity perpendicular to the 

 pipeline axis, witli the projected area in the plane parallel to the pipe- 

 line axis. 



After tabulating the data from the three-dimensional experiments, it 

 became apparent that the second method gave consistent values of the 

 coefficient of lift for all angles of orientation. In contrast, the values 

 of Cl obtained using the first method gave values that were low, and which 

 decreased with increasing angles of orientation (where 0° corresponds to 

 a pipeline parallel to the wave crests). 



Relationships between the coefficient of lift, Cl, and the parameters, 

 (}) and k, of the lift force equation were the same for all angles of orien- 

 tation when Cl was calculated considering only the component of the hori- 

 zontal velocities perpendicular to the pipeline axis. 



In addition, relationships involving any of the parameters of the lift 

 force equation (Cj^, <t>, or k) and various dimensionless parameters defining 

 the wave and pipeline conditions were consistent for all angles of orien- 

 tation when the horizontal water particle velocity acting on the pipe 

 section was treated by considering only the component perpendicular to the 

 pipeline, and completely ignoring the parallel component. 



Thus, the results of this investigation show that the modified lift 

 force equations presented in this report can be applied to pipelines 

 located at any angle of orientation with respect to the wave crests. 

 However, only the component of the horizontal water particle velocity 

 perpendicular to the pipeline axis should be considered as contributing 

 to the wave-induced lift force acting on the pipeline. Using this approach, 

 the parameters, Cl, ^, and k, defining the lift forces exhibit the same 

 quantitative relationships between the various dimensionless parameters de- 

 fining the wave and pipe conditions, regardless of the angle of orientation. 



75 



