14. The horizontal coefficient of mass, C|^], showed excellent 

 agreement with the potential flow solution for a circular cylinder in 

 the vicinity of a plane wall subject to a uniform flow with constant 

 acceleration. These results indicate that the potential flow solution 

 may be useful for selecting a value of Cf^^ for wave-induced forces, at 

 least for situations in which the inertial forces predominate over the 

 drag forces. The horizontal C^ was also correlated with several of the 

 dimensionless parameters defining the wave and pipeline conditions, 

 such as the parameter clear/Uj^^^^T. 



V. RECOMMENDATIONS FOR FURTHER RESEARCH 



1. Experiments similar to this investigation should be carried out 

 in a larger wave tank facility. This would allow the testing of larger 

 diameter pipeline models as well as experiments at higher Reynolds 

 numbers and higher values of the Keulegan-Carpenter parameter. Such 



an investigation is necessary to determine the validity of extrapolat- 

 ing the results of the present study to design situations in the ocean, 

 and to point out any weaknesses or limitations of the proposed lift 

 force model due to scale effects. 



2. It would be of interest to perform experiments to evaluate the 

 magnitude, phase, and frequency spectra of the vertical transverse 

 lift forces due to eddy shedding for a horizontal cylinder subject to 

 oscillatory horizontal flow velocities. This could be done by oscil- 

 lating a test cylinder horizontally in still water away from a boundary, 

 or by using a pulsating flume facility. The horizontal flow patterns 



at the bottom could be simulated, but without the lift force phenomenon 

 due to the boundary. Only the transverse lift forces due to eddy 

 shedding would act in the vertical direction, so the magnitude and time 

 history of these forces could be easily measured. 



A thorough analysis of the eddy forces for different pipe diameters 

 and flow conditions would allow an evaluation of their importance rela- 

 tive to the Bernoulli -type lift forces, and at the same time explain 

 some of the variations in the vertical wave force parameters calculated 

 from an analysis which neglected the eddy forces because they could 

 not be separated analytically because of their random nature. Adequate 

 knowledge of the eddy forces would allow the addition of the eddy lift 

 force term, F^ = 1/2 Cf^ p A u^^x^ ' ^° ^^® Morison equation with appro- 

 priate values of the coefficient C^ for any given set of wave and pipe- 

 line conditions. 



It sliould be noted that evaluation of the eddy forces for a cylinder 

 away from a boundary would only give an approximate estimate of the 

 eddy release phenomenon for a pipe located near the bottom. The presence 

 of the bottom boundary changes the flow pattern, velocities, and pressure 

 distribution around the cylinder, and therefore would be expected to 

 have some effect on the formation and release of eddies. 



121 



