(Yuksel and Narayanan, 1994a) is reasonably satisfactory for the wave
forces. However, the difficulty remains in the choice of appropriate drag
and inertia coefficients. When the waves approach the cylinder obliquely,
then the component of the velocity normal to the cylinder is applied in the
Morison equation to determine the wave force.
The incipient wave breaking for which the criteria are given by equa-
tions (14.41) and (14.42) coincides with the occurrence of the maximum
wave height showing the initiation of a bubble with attendant foam forma-
tion. At the later stage of plunging, the crest of the wave falls onto the
forward moving water. The wave height at the plunge point is about 60%
of that at the breaking point. Experimental studies concerning breaking
wave forces are available only for waves approaching normally to the
cylinder (Yuksel and Narayanan, 1994b). For horizontal cylinders fully
submerged in water and resting on a rigid beach, the maximum forces
occur when the cylinder is placed at the plunge point. The impingement
force on the cylinder placed at the plunge point is not a constant but
exhibits randomness; therefore a statistical measure of the breaking wave
force for certain probability of exceedence is used.
14.11.4 Pipeline stability
For the design of submarine pipelines in shallow waters the refraction
pattern of the wave has to be obtained. The direction of the waves with
respect to the pipeline is determined along the pipeline before the waves
break. In order to evaluate the wave forces on the pipeline the com-
ponents of the particle velocity and acceleration normal to the pipe axis
are used in the Morison equation. Very little is known about the forces on
the pipe once the waves break. Submarine pipelines, especially those in
shallow water, are normally buried. However, they may be allowed to rest
on the sea bed before burial. Sometimes the characteristics of the sea bed
may be such that neither burial nor anchoring is possible. In this case the
stability of the pipeline against rolling must be considered.
Referring to Fig. 14.20, the pipeline is subjected to the in-line
force due to the combined action of currents and waves, Fi, and the lift
forceFL(bothFiandFLare per unit length of the pipeline). Let the sub-
merged weight of the pipeline per unit length be W. For stability against
rolling
Fiμ(W FL)
whereμis the coefficient of friction for the seabed–pipeline interface.
So far in this section, linear theory has been used for fluid velocity
and acceleration. In deep water Stokes’ higher order theory should be
610 WAVES AND OFFSHORE ENGINEERING
