of these processes with the decreasing velocities of the passing wave 

 crest also involves a small but finite amount of time. Thus, there will 

 be a slight timelag in the point of maximum positive lift with reference 

 to the instant of maximum velocity as the wave crest (or trough) passes 

 over the reference point. The smaller the amount of positive lift rela- 

 tive to the amount of negative lift, and the later the positive lift 

 occurs in the wave cycle, the greater the timelag. 



An example of the lift force phenomenon over a complete wave cycle 

 for a small bottom clearance is shown in Figure 3. 



For a given pipe diameter and wave condition, as the bottom clearance 

 is increased, higher velocities are necessary to produce the choking 

 effect in which the flow becomes restricted through the bottom clearance 

 constriction. Thus, as the bottom clearance is increased, the flow under 

 the pipeline begins to become restricted closer to the approaching wave 

 crest or trough, where the horizontal velocities are at a maximum; this 

 choking effect also diminishes soon after the wave crest or trough has 

 passed. Therefore, as the bottom clearance is increased, the downvjard 

 lift force occurs during a larger part of the wave cycle. 



At the same time, larger clearances permit greater maximum velocities 

 and corresponding lower pressures under the pipe section. Since higher 

 flow rates are possible under the pipe section, less of the wave-induced 

 flow must be diverted over the top of the pipeline. As a result of 

 these changes, the negative lift forces reach a greater magnitude before 

 the choking effect begins, and these maximums are attained later in the 

 wave cycle. 



Correspondingly, the upward lift forces occur during a smaller part 

 of the wave cycle, and the maximum magnitude these forces attain decreases 

 with increasing bottom clearance. These maximum values are also reached 

 later in the wave cycle. 



If the clearance is increased further, a point is eventually reached 

 at which the clearance is large enough so that the choking effect does 

 not occur. At this stage, the velocities are higher through the bottom 

 clearance constriction than over the top of the pipeline during the 

 entire wave cycle. So the associated pressure distribution results in 

 a negative lift force throughout the wave cycle, with maximum downward 

 forces occurring under the crests and troughs of the passing waves. The 

 negative lift diminishes to zero at the points of horizontal flow reversal, 



As the bottom clearance is increased further, the downward lift effect 

 is gradually reduced. The phase of the force cycle relative to the wave 

 cycle remains the same, but the magnitude decreases. Eventually, a 

 point is reached where the bottom clearance no longer acts as a constric- 

 tion to the wave-induced flow. The flow pattern becomes approximately 

 symmetrical, and the increased velocities of the horizontal flow diverted 

 over the top and bottom of the pipeline, along with the corresponding 



24 



