Scattering of periodic surface waves by pile-group supported platform

A semi-analytical approach is proposed to solve the scattering of free surface waves around a platform supported by a pile array. Assuming periodic lattice configuration and strong contrast between cylinder spacing and typical wavelength, the multi-scale perturbation theory of homogenization is employed to derive the effective equations governing the macro-scale wave dynamics and the boundary-value problem of micro-scale flows within a unit cell. The constitutive coefficient in the macro-scale effective equations are computed from the solution of the micro scale boundary-value problem, which is driven by the macro-scale pressure gradient. Flow separation is treated by the eddy viscosity model where the bulk eddy viscosity is determined by balancing the time-averaged rate of dissipation and the rate of work done by wave forces on the cylinders integrated over the entire platform region. The proposed semi-analytical approach is validated by comparisons with laboratory experiments for a pile-group supported platform in a wave flume. In addition field-scald wave scattering by a pile-group supported circular platform is investigated. For long waves, the maximum vertical force exerted on pile-group supported platform may reach 1.2 times of the value without piles. The maximum increase of the torque in transverse direction occurs for intermediate waves, which may reach 40% for the parameters discussed.