A model test for the wave interaction with a four-cylinder structure

The prediction of the runup and free surface elevation is of great interest for the offshore industry, e.g. to determine the air gap. Air gap is the vertical distance from the underside of the platform deck to the wave crest. This clearance must be sufficient that the wave does not strike the lower deck. At the same time, it must also be minimized in order to avoid raising the centre of gravity and exposed vertical surface area of the platform, which may affect the wind loading and will increase the wind overturning moments. An important influence on the determination of air gap is the phenomenon known as near-trapping. For a multi-column structure this has been shown theoretically to occur at critical frequencies dependent upon the geometry of the structure. These phenomena can cause the local wave elevations to be significantly greater than that of the undisturbed incident wave. Considering arrays of vertical bottom mounted circular columns, the scattering of water waves by arrays of columns was solved exactly by Linton and Evans (1990). Subsequently Evans & Porter (1997) made a detailed investigation of near-trapping by circular arrays of vertical cylinders. Malenica et al. (1999) extended the studies of near-trapping in an array to the second-order and suggest that second-order near-trapping occurs when the frequency of the second-order components is equal to the frequency of first-order near-trapping. However predicted by theoretical study, the near-trapping phenomenon has rarely been experimentally verified. In the present study the diffraction of regular waves by an array of four vertical cylinders is investigated by a model test. The test was undertaken in a wave basin at Dalian University of Technology and designed to measure the free surface elevation η at multiple locations close to the body surface subjected to regular waves of the steepness kA varies from 0.06 to 0.10, where k is the wave number, A is the incident wave amplitude. Ohl et al. (2001) has carried out a similar experiment and outstanding results are obtained from the experiment. Due to model and facility constraints the experiment was conducted for 6 frequencies in the range 0.449<ka<0.555, where a is the cylinder radius. In the present test, a wider range of frequencies 0.408<ka<1.966 were employed and over this frequency range the near-trapping phenomenon both at the firstand the second-order can be investigated. As the near-trapping phenomenon is sensitive to the change in ka, tests were conducted for totally 30 frequencies and the frequencies are distributed densely in the range where near-trapping phenomena are theoretically predicted to occur. Firstand second-order terms of wave elevations are computed from the measured time series. It can be found that high localized wave elevations were observed at both the firstand second-order. The large increases in free surface elevations are found to occur over a range of frequencies, close to the near-trapping frequency. The results are then compared with those obtained by QTFDUT, a hydrodynamic analysis program developed in the frame of potential flow theory. It’s found that the potential flow theory can be effective at predicting the firstand second-order qualities. At most frequencies satisfying results can be obtained by using the linear diffraction theory alone. However, at some crucial frequencies, the magnitude of local free surface is affected by significant nonlinear interactions, and the second-order qualities make a considerable contribution.