sea bed and on the cylinder, dynamic boundary conditions on the free
surface and the radiation conditions at infinity. Numerical approaches
using Green functions (Garrison and Chow, 1972), the finite element
method (Bai, 1975) and boundary element methods (Brebbia, 1978) are
used to calculate s.
Oncesand hence Tare known, the pressures on the cylinder are
obtained from equation (14.6) without the hydrostatic pressure term.
Integration of the pressure distribution leads to the force on the cylin-
der. The variation of the dimensionless maximum in-line force
Fim/[ gHDdtanh(kd)/kd] as a function of kDfor a surface-piercing vertical
cylinder is shown in Fig. 14.19.
14.11.3 Wave forces on pipelines in the shoaling regionAs the waves move progressively towards the shore, the non-linear effects
have a significant effect on the wave height. The wave height of parallel
waves predicted by the finite amplitude wave theory can be larger than
that calculated by equation (14.33) from linear theory. Iwagaki, Shiota and
Doi (1982) propose a simple approximate expression for the wave height
in shoaling waters avoiding complex calculations of cnoidal wave theory.
Swift and Dixon (1987) present shoaling curves based on a stream function
series solution.
Wave forces exerted on horizontal cylinders parallel to wave crests
are calculated using the Morison equation (14.69) in the shoaling region
before wave breaking. The kinematics at the position of the cylinder for
the undisturbed wave should be determined by a finite amplitude theory
such as the streamfunction theory (Huang and Hudspeth, 1982). Labora-
tory experiments show that the cnoidal wave theory for wave kinematics
FORCES ON CYLINDRICAL STRUCTURES 609
Fig. 14.19 Maximum wave force on a large vertical cylinder