It is common practice to use Morison equation (14.63) for the in-line
force for co-existing waves and currents, by replacing the velocity compo-
nentuin equation (14.63) by the total velocity which is the algebraic sum
of the current velocity and the particle velocity due to the waves (see
Worked example 14.2).
If the axis of the cylinder is inclined at an angle to the direction of
wave propagation, then the velocity and the acceleration normal to the
axis are used in the Morison equation to obtain the force. The tangential
force exerted by the component of the velocity along the cylinder is relat-
ively small.
Vertical cylinders can experience the force of breaking waves. If the
height of the wave at breaking is Hb, the force exerted on the cylinder may
be expressed as
FBCB gDH^2 b. (14.68)
The coefficient CBis found to vary between 1.2 and 3.0.
(b) In-line forces on small horizontal cylinders
For a horizontal cylinder, the axis of which is parallel to the crest of the
wave, the force per unit length of the cylinder is, according to the Morison
equation,
FiCD
2
|u|uDCM. (14.69)
uand du/dtare perpendicular to the axis of the cylinder. In equation
(14.69),CDandCMagain depend on the Reynolds number, the Keulegan–
Carpenter number and the roughness, and also on the gap ratio G/D(Gis
the gap between the cylinder and the sea bed). Sarpkaya (1976b, 1977)
providesCMandCDagainstRefor various Kcand. CMfor frictionless
flow is 3.3 for a smooth cylinder resting on the sea bed (G/D0). Experi-
ments have been conducted by Littlejohns at Perrin Bay, Cornwall, UK, to
determine the values of the coefficients under field conditions (Littlejohns,
1982). Allowing for the scatter of the results, which is natural for the test
conditions, the appropriate values are CD1.0 and CM2.4 for cylinders
resting on the sea bed, with Kcup to 13.0.
(c) Transverse forces on small horizontal cylinders
In oscillatory flow the flow separates from the surface of the cylinder for
Kc3. For Kc5, vortices are shed asymmetrically from the top and
G
D
du
dt
πD^2
4
606 WAVES AND OFFSHORE ENGINEERING
