available over at least 30 years, long-term statistics are preferred. Extreme
value statistics are dealt with comprehensively by Goda (1979), Isaacson
and Mackenzie (1981) and Sarpkaya and Isaacson (1981).
14.11 Forces on cylindrical structures
14.11.1 Forces due to currents
Offshore structures constructed of cylindrical members and submarine
pipelines are exposed to hydrodynamic forces due to waves and currents. A
steady current approximated, for instance, by the tidal flow will exert
steady and fluctuating forces on the cylindrical structures. If the cylinder is
well away from solid boundaries, the forces are a steady in-line force
together with the fluctuating in-line and lift forces. On the other hand, a
pipeline resting on the sea bed will be additionally subjected to a steady lift
force acting away from the bed owing to the asymmetry of the flow struc-
ture. The effects of the fluctuating forces are discussed in Section 14.12.
Consider an isolated, smooth cylinder of diameter D, the axis of
which is normal to uniform flow. The steady in-line or drag force per unit
length of the cylinder FD, is customarily expressed as
FD
1
2
CD V^2 D (14.61)
whereCDis the drag coefficient. CDis a function of the Reynolds number
ReVD/+, where Vis the velocity upstream of the cylinder and +is the
kinematic viscosity of the fluid (Schlichting, 1960). CDdecreases with Re
for laminar flow in the boundary layer along the periphery of the cylinder.
AtRe≈ 105 (the precise value depending on the turbulence level of the
stream and the roughness of the cylinder), transition to turbulent flow in
the boundary layer takes place with an abrupt drop in the value of CD
(Schlichting, 1960).
The lift force or the force transverse to the direction of the current
per unit length of the cylinder is expressed similarly to equation (14.61) as
FL
1
2
CL^ V^2 D (14.62)
whereCLis the lift coefficient. Isolated cylinder experiences no steady lift
but a considerable fluctuating lift with a frequency equal to the shedding
frequency of vortices from the cylinder.
The forces exerted on a pipeline in the proximity of the sea bed are
dependent on the Reynolds number of the flow, the relative roughness of
602 WAVES AND OFFSHORE ENGINEERING
