In the following discussion, the wave run-up and wave force of the above cylinders with cosine-type perturbation cross-sections is analyzed considering the effects of the rotation angle, as defined in Fig. 2. As an example, the parameters of ε and ka0 are set as 0.05
and 2, respectively. Because the geometric shape of the cylinder in
the cases of nr = 1 is approximately similar to a circle, the effects of
the rotation angle are very small for such a geometrical shape.
Therefore, the following analysis focused mainly on the cases of
2 ≤ nr ≤ 5.
Fig. 11 shows the wave run-up profiles around the cylinders
under various rotational angles. The effects of the rotation angle
are very small for the case of nr = 2 because the configuration of
the cross-section is close to the circle. In this case, a very slight
variation of the wave run-up curves versus the rotation angle can be observed from Fig. 11(a) for the whole circle. For all of the geometrical shapes, the maximum wave run-up often occurs somewhere upstream. With the increase of nr , the variation of the
wave run-up of the upstream portion of the circle becomes more
obvious and is significantly affected by the more complex geo- metrical shape of the cylindrical surface, as shown in Fig. 11(b)-(d). From the analysis results, the wave run-up at the downstream part
of the cylinder, especially at the specific location near θ ¼ 0° (or
θ ¼ 360°), is not sensitive to the geometry of the cross-section
Fig. 12 shows the maximum dimensionless wave force in the x- and y-direction versus the rotational angle in one period. The
maximum wave force for the case of nr = 1 is almost equal to the
maximum wave force of the circular cylinder, which can be the
oretically proven to be 0.275 and 0 for FX
and FY , respectively. The
pared with Fig. 11c and d. When nr ≥ 3, the fluctuation varies with
rotation angle decrease and the wave force in both directions