Motivated by the development of new offshore platforms, a semi-analytical approach is proposed to solve the scattering of free surface waves around a two-dimensional platform supported by a pile array. The macroscale scattering is predicted based on microscale dynamics between piles. The flow field under platform is modelled by Reynolds equations with locally constant eddy viscosity. The open water region is solved by potential flow theory. Using homogenization theory, we obtain a generalized pressure equations in form of a Laplace equation with complex coefficients. By matching the normal velocity and pressure at the interfaces of open water regions and cylinder region, the macro-scale scattering (wave reflection and transmission) can be predicted based on micro-scale dynamics between piles efficiently.


Very large scale floating structures (VLFSs) supported by small piles are a common form of practical structures in coastal and offshore engineering (Kashiwagi, 2000), e.g. offshore airports, large storage facilities and wave energy converters (Singh and Babarit, 2014).

The scattering problems of non-viscous water waves by multiple bodies have been well resolved using different methods based on potential theory. In terms of the diffraction characteristics of single members, a general diffraction problem involving a number of separated bodies have been solved exactly (Kagemoto and Yue, 1986). Using multiple scattering technique, the full interaction phenomena between water waves and a multiple body array has been well solved using linear potential theory (Spring and Monkneyer, 1974; Simon, 1982; Linton and Evans, 1990). As the number of piles dramatically increases and more realistic flow conditions need to be considered, the aforementioned approaches become prohibitive and infeasible. Particularly, viscous effects may significantly affect the wake regions of each member in the pile array and dissipate the wave energy along the floating bodies. Combining the viscous flow model in the pile array region and non-viscous flow model outside seems to be a compromise approach. Even though, three dimensional viscous computational fluid dynamics is not suitable for practical purpose yet, when there are hundreds or even more piles in the array.

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