large lift forces. Transverse forces have been observed 4.5 times greater 

 than the drag force. 



For rigid structures, however, transverse forces equal to the drag force 

 is a reasonable upper limit. This upper limit pertains only to rigid 

 structures', larger lift forces can occur when there is dynamic interaction 

 between waves and the structure (for a discussion see Laird (1962)). The 

 design procedure and discussion that follow pertain only to rigid structures. 



Chang (1964), in a laboratory investigation, found that eddies are shed at 

 a frequency that is twice the wave frequency. Two eddies were shed after 

 passage of the wave crest (one from each side of the cylinder), and two on the 

 return flow after passage of the trough. The maximum lift force is pro- 

 portional to the square of the horizontal wave-induced velocity in much the 

 same way as the drag force. Consequently, for design estimates of the lift 

 force, equation (7-44) may be used: 



F, = F cos 29 = C ^ DH^K cos2e (7-44) 



1- Lm Z, z Dm 



where F^ is the lift force, F. is the maximum lift force, 



L Lm 



9 = (2irx/L - 2iit/T) , and C, is an empirical lift coefficient analogous to 



the drag coefficient in equation (7-38). Chang found that C, depends on the 



Keulegan-Carpenter (1956) number u T/D , where u is the maximum 



max max 



horizontal velocity averaged over the depth. When this number is less than 3, 



no significant eddy shedding occurs and no lift forces arise. As u T/D 



mxx 



increases, C, increases until it is approximately equal to C (for rigid 



Li U 



piles only). Bidde (1970, 1971) investigated the ratio of the maximum lift 



force to the maximum drag force F^ /F^^ which is nearly equal to C,/C„ if 



there is no phase difference between the lift and drag force (this is assumed 



by equation (7-44)). Figure 7-84 illustrates the dependence of ^fl^n ^"^ 



u T/D . Both Chang and Bidde found little dependence of C, on Reynolds 

 max _ ^ 



number R = u D/v for the ranges of R investigated. The range of 



e max & 



R investigated is significantly lower than the range to be anticipated in 



the field, hence the data presented should be interpreted merely as a guide in 



estimating C, and then F, . 



The use of equation (7-44) and Figure 7-84 to estimate lift forces is 

 illustrated by the following example. 



*************** EXAMPLE PROBLEM 22************** 

 GIVEN: A design wave with height H = 3.0 m (9.8 ft) and period T = 10 



7-133 



