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

 shed at a frequency 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 proportional 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 7-37 may be used. 



pg 

 Fl = ^Lm '°'^^ = ^L^ DH^K^m ^°« 20. (7-37) 



where Fj^ is the lift force, F^^ is the maximum lift force, e = 

 (Zttx/L - 2TTt/T) , and C^^ is an empirical lift coefficient analogous to 

 the drag coefficient in Equation 7-31. Chang found that C^; depends on 

 the Keulegan-Carpenter (1956) number u^ax ^^^ where u^^ix ^^ ^^® 

 maximum horizontal velocity averaged over the depth. When this number is 

 less than 3, no significant eddy shedding occurs, and no lift forces arise. 

 As ^ax ^/^ increases, C^ increases until it is approximately equal 

 Cj) (for rigid piles only). Bidde (1970, 1971) investigated the ratio of 

 the maximum lift force to the maximum drag force Fi,m/Fj)m which is 

 nearly equal to Cj^/C^ if there is no phase difference between the lift 

 and drag force (this is assumed by Equation 7-37). Figure 7-56 illus- 

 trates the dependence of C^/Cj) on ^rnax T/D. Both Chang and Bidde 

 found little dependence of C^ on Reynolds Number Rg = u^^^ D/v for 

 the ranges of Rg investigated. The range of Re 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 Vj^ . 



The use of Equation 7-37 and Figure 7-56 to estimate lift forces is 

 illustrated by the following example. 



************** EXAMPLE PROBLEM *************** 



GIVEN : A design wave with height, H = 10 ft. and period, T = 10 sec. 

 acts on a vertical circular pile with a diameter, D = 1 ft., in a 

 depth, d = 15 ft. Assiome C^^ = 2.0 and C^ = 0.7. 



FIND : The maximum traverse (lift) force acting on the pile and the 

 approximate time variation of the transverse force assuming that 

 Airy theory adequately predicts the velocity field. Also estimate 

 the maximum total force. 



7-96 



