Although the eddy- induced component of the vertical wave force may 

 be significant when compared to the relatively small vertical drag and 

 inertial forces, the experimental results of this investigation show 

 that the eddy-induced lift forces are much smaller than the "Bernoulli- 

 type" lift forces for pipelines located near the bottom. At large 

 clearances above the bottom where the Bernoulli-type lift effect becomes 

 negligible, the transverse lift forces due to eddy shedding may become 

 a significant component of the total vertical force. At the same time, 

 as the pipeline is raised farther from the bottom boundary, the verti- 

 cal inertial and drag forces also become more significant. 



The vertical component of the total wave-induced force acting on a 

 pipeline near the ocean bottom thus consists of four components --the 

 lift force, the inertial force, the drag force, and the transverse lift 

 force due to eddy shedding. Using the Morison approach, the total ver- 

 tical wave force is expressed as the sum of these components: 



•'* 



where F^ is the lift force and F ' is the transverse lift force due to 

 eddy shedding. 



2. Wave-Induced Lift Forces . 



Consider a pipeline in contact with a horizontal rigid, impervious 

 bottom. Water cannot flow between the pipe and the bottom boundary, so 

 the flow must be diverted over the top of the pipe. The asymmetrical 

 distortion of the flow field results in maximum velocities over the top 

 of the pipe section and minimum velocities over the bottom, with zero 

 velocities at the stagnation point on the upstream side of the pipe 

 bottom at the point of contact with the sea floor. Correspondingly, 

 the associated pressure distribution will induce an upward lift force 

 for any velocity field acting on the pipeline. The stagnation pressure 

 at the bottom of the pipe section will increase with increasing veloc- 

 ity, while simultaneously the pressure distribution over the top of the 

 pipeline will decrease with the increased velocities of the flow di- 

 verted over tne top of the pipe section. The wave-induced lift forces 

 will thus act in the upward direction throughout the wave cycle, in- 

 creasing with the horizontal water particle velocities to maximum mag- 

 nitudes under the crests and troughs of the passing waves, and 

 diminishing to zero at the points of horizontal flow reversal. 



In contrast, a pipeline located at a small clearance above the 

 bottom boundary is subject to a more complex type of lift phenomenon. 

 At the phase in the wave cycle where the horizontal component of the 

 water particle velocity reverses direction, the horizontal velocity 

 over the pipeline is approximately zero. As the wave crest or trough 

 begins to approach the pipeline, the wave-induced horizontal velocities 

 are initially low, inducing unrestricted flow at low velocities over 

 both the top and bottom of the pipeline. However, the water flows 



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