Hydraulic Structures: Fourth Edition

bottom of the cylinder causing alternate transverse or lift forces normal to
the oscillatory flow direction. Transverse forces can be of similar magni-
tude to the in-line forces. The oscillatory flow reverses its direction in
every half cycle and the flow has to adjust to this reversal. The flow struc-
ture is complex with some vortices interacting with the cylinder when they
are swept back and forth. The dominant frequency of the lift force
increases with the Keulegan–Carpenter number. It is the same as the wave
frequency for Kc5, the second harmonic of the wave frequency for
5 Kc15 and the third harmonic for 15Kc20 and so on. At Kc
numbers greater than about 25, the fluctuating lift coefficient tends to
attain a value typical of the steady flow and the wake resembles a steady
flow Karman Vortex street.
The lift force per unit length of the cylinder FLis usually presented as:

FL

1

2

CL^ u^2 D

whereCLis the lift coefficient. Sarpkaya (1976a) presents CLin terms of Kc
andRefor smooth cylinders exposed to periodically oscillated flow in a
U-tube (Fig. 14.18). Further experiments of Sarpkaya (1976b) provide
values of the lift coefficient for cylinders above a plane bed.
No accurate representation of the lift force variation with time in
oscillatory flows has been achieved. Chakrabarti (1987) represented the
lift force for vertical cylinders by a Fourier series having frequencies equal
to the wave frequency and its multiples as:

fy(t)

1

2

 u^2 D

N

n 1

CLncos(nt (^) n) (14.70)

FORCES ON CYLINDRICAL STRUCTURES 607

CL

4

0

0.1 15

Re. 105

1

3

2

KC 15

0.5 1. 2. 3. 4. 5. 10

60

40

30

20

Fig. 14.18 Lift coefficient as a function of Reynolds number for various
values of KCfor smooth circular cylinder (Sarpkaya, 1976a)