pressure distribution, become approximately equal over both sides of the 

 pipe section. At this point, the lift effect is no longer present, and 

 the lift force term may be neglected in calculating the wave-induced 

 forces acting on the pipeline. 



The transition in the lift force cycle with increasing bottom 

 clearance is shown in Figure 4. 



3. Model for Wave-Induced Lift Forces . 



The traditional lift force equation, derived for unidirectional 

 steady-flow situations, is expressed as Fl = 1/2 Cl P A u^, where Cl is 

 the coefficient of lift. This equation has been applied to wave-induced 

 lift forces, using the horizontal component of the oscillating water 

 particle velocity, u, in the relationship. The lift force expressed in 

 this way assumes that the force acts in one direction only (either upward 

 or downward) throughout the entire wave cycle. 



A pipeline located on the ocean floor with no clearance will 

 experience an upward lift force throughout the entire wave cycle, 

 increasing with the horizontal velocities to reach maximum values under 

 the crests and troughs of the passing waves, and diminishing to zero 

 as the horizontal velocities go to zero at the point of flow reversal. 

 This phenomena is described adequately by the above lift force equation 

 with a positive coefficient of lift Cl- 



A pipeline located at a large enough clearance above the bottom so 

 that the choking effect does not occur will experience a downward lift 

 force throughout the wave cycle, since the flow is always faster through 

 the bottom constriction than over the top of the pipeline. Again, this 

 negative lift force increases with the horizontal water particle veloci- 

 ties, reaching maximum magnitudes under the crests and troughs of the 

 passing waves, and decreasing to zero as the flow reverses. This phe- 

 nomenon is also suitably expressed by the traditional lift force equation, 

 but using a negative coefficient of lift. 



These two situations represent the extreme cases bounding the lift 

 force phenomena. However, the choking phenomenon will occur at any 

 clearance between these two limits, and the traditional lift force 

 equation cannot be used to accurately describe the forces exerted on 

 a pipeline. This equation must be replaced by a model developed speci- 

 fically for wave-induced lift forces. The experimental results of this 

 investigation demonstrate that the largest wave-induced lift forces 

 occur at these intermediate clearances, where the choking phenomenon 

 does develop. 



Since the lift force phenomenon is repeated twice per wave cycle 

 with the reversal of the horizontal flow pattern, the lift force can 

 be described mathematically by a sinusoidal function of twice the fre- 

 quency of the waves. In addition, the mathematical expression must 

 allow for description of the following lift force properties: 



26 



