Wave-Induced Eddies and "Lift" Forces on Circular Cylinders 



F, = F„ + F„ 



h Dh Ih 



(4) 



with 



F„, = — P C n D 

 Dh 2 D 



(5) 



and 



„ n ttD bu 



F ih = pC m ~t ~oT 



(6) 



where u u is used rather than u to account for direction of 

 flow. Fqi is the horizontal drag force per unit length of cylinder, 

 Fjk is the horizontal inertia force per unit length of cylinder, Cw 

 is the coefficient of mass, Cq is the coefficient of drag, D is the 

 cylinder diameter. o'u/ dt is used in place of du/dt when the dia- 

 meter of the cylinder is small compared with the wave length. 



When the Keulegan-Carpenter number is sufficiently large 

 that eddies form, an oscillating "lift" force will occur. For a verti- 

 cal pile the "lift" (transverse) force will be in the horizontal plane 

 normal to the direction of the drag force. Few data have been publish- 

 ed on the coefficient of lift, Cj^ , for water wave type of flow 

 (Chang, 1964 ; Bidde, 1970 ; 1971). In uniform rectilinear flows it 

 can be as large as Cjp , although there are few results available 

 (Laird, 1961). The horizontal "lift" force per unit length of cylinder 

 is given by 



Lh 



= T " c l d 



(7) 



where C^ is the coefficient of "lift". 



Photographs taken of flow starting from rest, in the vicinity 

 of a circular cylinder for the simpler case of a non-reversing flow, 

 show that it takes time (the fluid particles must have time to travel a 

 sufficient distance) for separation to occur and eddies to form (Rouse, 

 1946, p. 240). The effect of time on the flow, and hence on C D and 

 C M has been studied by Sarpkaya and Garrison (1963 ; see also 



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