As the wave crest or trough passes, this series of steps in the 

 lift force phenomenon is reversed. The horizontal velocities approach- 

 ing the pipe section begin to decrease, resulting in a decrease in the 

 positive- lift force exerted on the pipeline. As the velocities decrease 

 further with the passing wave, the flow londer the pipe section begins 

 to become less restricted. The choking effect thus decreases, and the 

 turbulence and eddies near the bottom clearance gradually diminish. As 

 the flow under the pipe section ceases to be restricted, less of the 

 horizontal flow approaching the pipeline is forced to flow over the top 

 of the pipe, so the stagnation point will accordingly shift upward, 

 closer to the center of the pipe section. 



The flow velocities decrease simultaneously over the top and bottom 

 of the pipeline as the wave passes, but the rate of decrease is faster 

 over the top of the pipe than in the vicinity of the bottom constric- 

 tion. The positive lift force decreases until eventually, the flow 

 velocities, location of the stagnation point, and associated pressure 

 distribution are such that the pressure integrated over the pipe sec- 

 tion again results in a negative lift force. The downward lift force 

 then increases as the flow through the bottom clearance becomes less 

 restricted with the decreasing velocities of the passing wave. 



This lift phenomenon, as shown in Figure 2 for a passing wave crest, 

 is repeated twice during each wave cycle as the direction of the wave- 

 induced horizontal velocities reverses under the crests and troughs of 

 the passing waves. 



In reality, the horizontal flow reversal occurs almost instanta- 

 neoiosly, so the negative lift force does not return to zero at the 

 point of zero velocity when the flow reverses through the bottom clear- 

 ance constriction. The instant of zero velocity occurs only at the 

 center of the pipe cross section (the reference point) . Since the 

 pipeline has a finite diameter, the wave- induced flow acting on the 

 pipe section at any instant includes the sum of the flow condi- 

 tions induced by the part of the wave covering the entire diameter of 

 the pipeline. So instead of going to zero with the passing wave crest, 

 and then increasing initially with the approaching trough, the lift 

 force remains negative during the period of minimal velocities as the 

 flow reverses under the pipe section. 



In a similar manner, the lift force does not become positive as 

 soon as the choking effect occurs in the bottom clearance constriction. 

 The development of the choking phenomenon involves the formation of a 

 turbulent jet through the constriction, and a downward shift in the 

 stagnation point as more water is diverted over the top of the pipe 

 with increasing restriction of the flow through the clearance. The 

 corresponding changes in the velocities, flow pattern, and associated 

 pressure distribution over the top and .bottom of the pipe section pro- 

 duce the transition from negative to^ positive lift. This process 

 requires some small but finite amount of time. Conversely, the reversal 



22 



