(a) The lift force may be positive during part of the wave cycle 

 and negative for the rest of the cycle. The proportion of positive lift 

 to negative lift may range from all positive lift to all negative lift. 



(b) The positions of the maximum values of both the upward and 

 downward lift forces will shift with respect to the position of the 

 wave cycle as the bottom clearance is increased (for a given pipeline 

 and wave condition) . 



(c) As the clearance is increased, the maximum value of the upward 

 lift force will decrease, while correspondingly the maximum value of 

 the downward lift force will increase. 



(d) When the bottom clearance is increased to a point at which the 

 lift effect is downward throughout the entire wave cycle, further 

 increases in clearance will result in decreases in the maximum magnitude 

 of the downward lift force, but without a shift in the position of the 

 maximum lift force with respect to the position of the wave cycle over 

 the pipeline. 



A lift force equation of the form. 



= 1/2 Cl P a u^ax'[cos' [Q - <P) - k], (4) 



allows an adequate mathematical description of all the above properties 

 of the wave-induced lift force phenomena. This equation fits the experi- 

 mental data reasonably well over the wide range of conditions tested. 



The parameters involved in this modified form of the traditional 

 lift force equation are: 



Cl = coefficient of lift 



p = mass density of fluid 



A = projected area of pipe section 



^max ~ maximum value of horizontal component of water 

 particle velocity at center of pipe section if 

 pipeline was absent 



2Trt 

 9 = — =— = position of wave cycle over cen1:er of pipe section 



with respect to time, where T is the wave period 



and t is the time since the last crest passed over 



the center of the pipe section (see definition 



sketch in Fig. 5) . The wave crest corresponds to 



= 0° (0 radians) or -2TTt/T = radians. The wave 



trough corresponds to 180° (tt radians) or 



2TTt/T = TT radians 



28 



