# Nonlinear wave interaction with a vertical circular cylinder. Part I: Diffraction theory

##### Citations

115 citations

106 citations

### Cites background or methods from "Nonlinear wave interaction with a v..."

...The main purpose of this case is to provide a comparison between the OF prediction and theoretical models which are based on linear and second-order diffraction theory (see Kriebel, 1998), as well as reported experimental work (see Kriebel, 1998)....

[...]

...7%, as described by Kriebel (1998). Fig. 15 also illustrates the OF prediction with second order Stokes wave boundary condition, the OF prediction agrees with the experiment at the maximum force is predicted within 0.5% and the mean force is predicted within 15%. In comparison with second-order theory, OF agrees well; the maximum force is predicted within 0.4% and the mean force is predicted within 0.5%. The nonlinearities are the result of dominance of the second order plane wave components and are common features of nonlinear inertial forces experienced at small kr < 0.4, as discussed by Kriebel (1998). A small difference in the result is expected because the physical data is averaged over 10 wave periods, whereas the numerical result represents one wave cycle only once a steady state has been reached....

[...]

...More recently, second-order theories (Kriebel, 1998, Rahman and Heaps, 1983 and Taylor and Hung 1987), which consider the nonlinearity and can give more accurate wave force predictions, were proposed....

[...]

...The nonlinearities are the result of dominance of the second order plane wave components and are common features of nonlinear inertial forces experienced at small kr 0.4, as discussed by Kriebel (1998)....

[...]

...…simulated an oscillating water column device in waves by solving the Navier Stokes equations with the level set method for the free surface, and Boccotti et al. (2012), Boo (2002, 2006), Dixon et al. (1979), Chaplin et al. (1997) and Kriebel (1998) have also investigated wave forces on structures....

[...]

101 citations

100 citations

### Cites methods from "Nonlinear wave interaction with a v..."

...Another method of obtaining the second-order forces is the direct integration of the pressure over the body surface up to second order (e.g. Chau 1989; Kim & Yue 1989; Scolan & Molin 1989; Kriebel 1990)....

[...]

78 citations

### Cites methods from "Nonlinear wave interaction with a v..."

...They found that linear diffraction theory is inadequate and used the superposition method of Kriebel (1992), which was still found inadequate for their regime of interest (Table 1), although it did give an improvement of linear diffraction theory....

[...]

...Extension of diffraction theory to the second order has been carried out by several other authors (Kriebel, 1990; Martin et al., 2001), using different approaches....

[...]

...…first kind and bm ¼ 1; m ¼ 0 bm ¼ 2ð−1Þmim; mN0 k ¼ 2k=L; wave number The run-up Ru(θ) around the cylinder is the maximum value of η. Extension of diffraction theory to the second order has been carried out by several other authors (Kriebel, 1990; Martin et al., 2001), using different approaches....

[...]

##### References

4,525 citations

2,339 citations

2,003 citations

[...]

1,244 citations