APPENDIX A 

 LEAST SQUARES ANALYSIS OF EXPERIMENTAL DATA 



Using Morison's method for the calculation of wave forces on a 

 pipeline, the vertical component of the wave-induced force may be 

 expressed as: 



Fv = (Fl)^ + (Fd)^ ^ Fl + f[ 



= Cm P V 1^ + 1/2 Cd p A V |v| 



+ 1/2 Cl P a u^ax' [cos^ (6 - 4.) - k] 



+ 1/2 C[ p A u^^^^ • ^^^^ 



Since the transverse lift force associated with eddy shedding (F^) is 

 a random phenomenon, there is no way to handle its time history in 

 analyzing a wave force record with several other forces occurring 

 simultaneously. Because the Bernoulli-type lift forces were much 

 larger than the eddy-associated forces for a pipeline located close to 

 the bottom, the eddy-associated lift force term was dropped from the 

 analysis. 



The vertical components of the water particle velocities and 

 accelerations near the bottom are small in comparison with the corre- 

 sponding horizontal components. As a result, the vertical lift forces 

 due to the horizontal components of the water particle velocities are 

 generally much larger than the vertical drag and inertial forces. The 

 drag forces are especially insignificant since the vertical excursions 

 of the water particles near the bottom are smaller than the diameter 

 of the pipeline. 



Using linear wave theory, the kinematics of the wave-induced water 

 particle motions with respect to time can be expressed as: 



ttH 



, ,2-n-z. 

 cosh (— j— J 



T . , ,2TTd. 

 smh ( J 



cos 6 (A2) 



ttH 



7772 



sinh (^V— ) 



T . . ,27Td, 



sinh (— j— J 



25 



sin e (A3) 



