FORCES EXERTED BY WAVES ON A PIPELINE 

 AT OR NEAR THE OCEAN BOTTOM 



by 

 George L. Bowie 



I. WAVE FORCE ANALYSIS 



1 . Wave Force Components on Pipelines Near the Bottom . 



The most common method of analyzing wave forces on pipelines is 

 the application of the Morison equation (Morison, et al., 1950). Using 

 this approach, the total wave- induced force on a pipeline can be broken 

 into several components, depending on whether the components are due to 

 the water particle velocities or accelerations. These force components 

 can, in turn, be separated into horizontal and vertical components 

 by using the horizontal and vertical components of the water particle 

 velocities and accelerations in their respective force equations. 

 Where there is no lift effect and no eddy-induced forces, the vertical 

 component, Fy, of the total wave force is 



Fv = CFi)^ + (Fd)^ = Cm P V ||- + 1/2 Cd P a v|v| (1) 



and the horizontal component, F|^, is 



Fh == (Fi)^ + (Fd)j^ = Cm P V II + 1/2 Cd P a u|u| , (2) 



where 



(Fj) = vertical component of inertial force 



(Fl), = horizontal component of inertial force 



(Fq) = vertical component of drag force 



(Fq), = horizontal component of drag force 



v = vertical component of water particle velocity if 

 pipeline was absent 



u = horizontal component of the water particle velocity 

 if pipeline was absent 



8v 

 8t 



vertical component of water particle acceleration 

 if pipeline was absent 



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