in which a0 is the radius of circular section and ε is the pertur
bation value of the radius. With the defined radius function, the
increase of the parameters
nr and ε. As an example, Fig. 3 shows
five types of cross-section under the condition of ε = 0.05 and
increasing nr .
An analytical study based on the perturbation theory and a
numerical study based on Green's theory were investigated by
Mansour et al. (2002) to determine the wave action on such types
of cylinders subjected to a train of regular waves. The results of the
maximum dimensionless wave force and wave run-up by the