7 The scaled boundary ﬁnite-element method (SBFEM) is a novel semi-analytical method 8 developed in the elasto-statics and elasto-dynamics areas that has the advantages of com- 9 bining the ﬁnite-element method with the boundary-element method. The SBFEM method 10 weakens the governing differential equation in the circumferential direction and solves the 11 weakened equation analytically in the radial direction. It has the inherent advantage of 12 solving the unbounded ﬂuid dynamic problem. In this paper, the boundary-value problem 13 composed of short-crested waves diffracted by a vertical circular cylinder is solved by 14 SBFEM. Only the cylinder boundary is discretized with curved surface ﬁnite-elements on 15 the circumference of the cylinder, while the radial differential equation is solved completely 16 analytically. The computation of the diffraction force based on the present SBFEM solu- 17 tion demonstrates a high accuracy achieved with a small number of surface ﬁnite-elements.

Scaled boundary FEM solution of short-crested wave

Scaled boundary FEM solution of short-crested wave diffraction by a vertical cylinder

In this article, a range of problems and theories will be introduced that will build towards a new wave energy converter (WEC) concept, with the acronym 'ROTA' standing for resonant over-topping absorber. First, classical results for wave power absorption for WECs constrained to operate in a single degree of freedom will be reviewed and the role of resonance in their operation highlighted. Emphasis will then be placed on how the introduction of further resonances can improve power take-off characteristics by extending the range of frequencies over which the efficiency is close to a theoretical maximum. Methods for doing this in different types of WECs will be demonstrated. Coupled resonant absorbers achieve this by connecting a WEC device equipped with its own resonance (determined from a hydrodynamic analysis) to a new system having separate mass/spring/damper characteristics. It is shown that a coupled resonant effect can be realized by inserting a water tank into a WEC, and this idea forms the basis of the ROTA device. In essence, the idea is to exploit the coupling between the natural sloshing frequencies of the water in the internal tank and the natural resonance of a submerged buoyant circular cylinder device that is tethered to the sea floor, allowing a rotary motion about its axis of attachment.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsta.2011.0165

Wave energy extraction by coupled resonant absorbers

Under the assumptions of the linearized theory of small-amplitude water waves, it is proved that plane waves, normally incident upon a semi-immersed cylinder of uniform circular cross-section floating freely on the surface of a fluid of infinite depth, are capable of being totally reflected. Numerically, this is shown to occur at a single non-dimensional frequency. This remarkable result is used to construct examples of motion-trapped modes, involving pairs of freely floating cylinders moving either in phase or out of phase. The former case is equivalent to having a motion-trapped mode for a single such cylinder next to a rigid vertical wall. In the latter out-of-phase case, the pair of cylinders move as if they form the wetted sections of a single rigidly connected catamaran structure.

Water-wave trapping by floating circular cylinders

Computer models based on the two-dimensional (2-D) elliptic mild-slope equation are nowadays routinely used in harbor engineering applications. However, structures like floating breakwaters and docks, which are often encountered in the modeling domain, render the problem for locally three-dimensional model and hence are problematic to incorporate in a 2-D model. Tsay and Liu (Applied Ocean Research. 1983. Vol 5(1): 30–37) proposed a highly simplified but approximate approach that does not violate the overall two dimensionality of the problem. The validity of their approach is examined in detail, and it is found that although their approximation provides results with the correct trend, the actual solutions deviate considerably from the theoretical solutions. We have developed correction factors that may be used to produce more reliable results using the framework of Tsay and Liu. Application of the resulting method to a harbor in Alaska shows that docks in the harbor distort the wave field considerably and...

A.G. Dixon

Papers

The scattering of regular surface waves by a fixed, half-immersed, circular cylinder