<p = phase shift of maximum lift forces with respect 



to wave cycle 



k = negative fraction of lift force cycle 



The parameter, k, represents the increase in the magnitude and 

 duration of the negative lift forces acting on a pipeline with increas- 

 ing bottom clearance, and the ' corresponding decrease in the magnitude 

 and duration of the positive lift forces. The value of k varies from a 

 minimum of to a maximum value of 1 . k = corresponds to the case of 

 a pipeline lying on the bottom with no clearance, in which the lift 

 forces are positive throughout the wave cycle, k increases with 

 increasing bottom clearance to a maximum value of 1, which corresponds 

 to the case of a pipeline located at a sufficient clearance from the 

 bottom so that the choking phenomenon does not occur, and in which the 

 lift forces are therefore negative throughout the wave cycle. 



The phase shift parameter, (j), represents the shift in the position 

 of the maximum values of both the positive and negative lift forces 

 with respect to the wave cycle as the bottom clearance increases. The 

 value of (f) may range from 0° to a maximum value of 90°. (j) = 0° corre- 

 sponds to the case of a pipeline located on the ocean floor with no 

 bottom clearance, in which the lift forces are positive throughout the 

 wave cycle with maximum forces occurring under the crests and troughs 

 of the passing waves. 4) increases with increasing bottom clearance to 

 a maximum value of 90°, corresponding to a pipeline located above the 

 bottom at a sufficient clearance so that the choking effect does not 

 occur; the lift forces are negative throughout the wave cycle with maxi- 

 mums occurring under the crests and troughs of the waves. As defined, 

 (J) = 0° when k = 0, and (p = 90° when k = 1, or vice versa. 



The coefficient of lift, Cl, in this form of the lift force equation 

 will always have a positive value, since negative values of the lift 

 force are accounted for by the value of the parameter, k. The lift 

 force equation is shown graphically in Figure 6. 



To apply the lift force equation to a practical design situation, 

 values of C^, k, and (J) must be determined for a given set of pipeline 

 and wave conditions corresponding to the particular case under considera- 

 tion. Selection of the appropriate values requires quantitative knowl- 

 edge of the functional relationships between these parameters and the 

 wave conditions, bottom clearance, and pipeline size and configuration. 

 The development of these relationships was the purpose of the experimen- 

 tal part of this investigation. 



In a real situation, a pipeline on the ocean floor is often laid over 

 an irregular bottom, supported by the high points in the bottom topography 

 but probably spanning the depressed areas.. In this case, the pipeline 

 must be broken into component sections of the same approximate bottom 

 clearance for a separate analysis of each section. The results of the 



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