Su 



at 



horizontal component of water particle acceleration 

 if pipeline was absent 



A = projected area of pipe section 



V = volume of fluid displaced by pipe section 



p = mass density of fluid 



Cy = coefficient of mass 



Cn = coefficient of drag 



For a pipeline located near the ocean bottom, the water particle 

 orbits are flattened parallel to the boundary. Assuming a horizontal 

 bottom, the vertical motions of the water particles are small in com- 

 parison to the horizontal motions, especially in shallow-water depths 

 relative to the wavelength. As a result, the vertical components of 

 the water particle velocities and accelerations are much smaller than 

 the horizontal components, and correspondingly the vertical components 

 of the drag and inertial forces will be smaller than the analogous 

 horizontal forces. 



Since the water particles at the bottom are effectively oscillating 

 in a horizontal plane, the vertical excursions of the water particles 

 will generally be less than the diameter of a submarine pipeline lying 

 on or near the bottom. Therefore, the vertical drag forces are 

 generally insignificant, and could probably be neglected from the 

 vertical wave force equation. 



Pipelines near the bottom are subject to vertical lift forces. 

 These forces are the result of the asymmetric distortion of the flow 

 field due to the proximity of the bottom boundary, which induces dif- 

 ferences in the horizontal flow velocities and corresponding pressure 

 distribution over the top and bottom of the pipeline. Since the water 

 particle velocities near the bottom are at a maximum in the horizontal 

 plane, the lift forces induced by these horizontal motions will gener- 

 ally be the predominant force acting in the vertical direction. 



Transverse "lift" forces due to eddy shedding may also be an 

 important component of the vertical wave force, since these forces are 

 also due to the horizontal water particle velocities and excursions 

 which are maximum in the horizontal direction. Certain values of the 

 Keulegan-Carpenter parameter and Reynolds number must be attained for 

 the eddy release phenomenon to occur. The proximity of the bottom 

 boundary will probably have some effect on the formation and release 

 of the eddies, both because it is a solid boundary, and because it 

 affects the orbital motions of the water particles induced by the 

 wave action. 



