faster through the bottom clearance constriction than over the top of 

 the pipeline, so the corresponding differences in the pressure distri- 

 bution exert a downward (negative lift) force toward the bottom bound- 

 ary (Fig. 1, a) . 



At first, the negative lift force will increase with the increas- 

 ing horizontal water particle velocities of the approaching wave, since 

 the flow velocities increase at a faster rate through the bottom clear- 

 ance constriction than over the top of the pipeline, thus producing 

 larger differences in the corresponding pressure distributions over the 

 top and bottom of the pipe section (Fig. 1, b) . 



This continues until viscous effects begin to restrict the flow 

 through the narrow bottom clearance. For a given small clearance and 

 a given amount of energy in the horizontal water particle velocities 

 approaching the pipeline, the velocities and flow rates of a viscous 

 fluid through the bottom clearance constriction can attain only certain 

 maximum values. Thus, a "choking" effect is exerted on the restricted 

 flow through the small bottom clearance, and the remainder of the wave- 

 induced flow is forced to flow over the top of the pipe section. Cor- 

 respondingly, the stagnation point will shift downward, increasing the 

 pressure on the lower upstream side of the pipeline. The larger the 

 proportion of the flow diverted over the top of the pipe, the lower the 

 stagnation point. 



At the same time, the increasing velocities associated with the 

 approaching wave crest cause the restricted flow through the bottom 

 clearance to form a turbulent jet with the generation of eddies behind 

 the jet. The generation of increased turbulence and eddies results in 

 an energy loss in the water flowing through the bottom constriction, 

 decreasing the velocities under the pipe section behind the jet. 



The above effects associated with the choking phenomenon limit the 

 maximum flow velocities and minimum pressures under the bottom side of 

 the pipe section. In contrast, the unrestricted flow velocities over 

 the top of the pipeline increase freely with the increasing horizontal 

 velocities of the advancing wave. The increased part of the approach- 

 ing flow that is diverted over the top of the pipe section due to the 

 shift in stagnation point produces a further increase in the flow 

 velocities over the top. Correspondingly, the pressure distribution 

 over the top side of the pipeline decreases at a faster rate than the 

 associated pressures along the bottom side, so the negative lift force 

 gradually decreases and eventually becomes positive (Fig. 1, c, d, and 

 e). 



At this stage, the upward lift force becomes larger as the hori- 

 zontal velocities acting on the pipeline increase further with the 

 advancing wave crest or trough (Fig. 1, f). 



20 



