Step approximation of water wave scattering caused by tension-leg structures over uneven bottoms

The scattering of water waves induced by tension leg structures (TLSs) over uneven bottoms is investigated using the eigenfunction matching method (EMM). Both the wave amplitude and the surge-motion displacement were assumed to be small, and the linear wave theory was employed to solve the problem. In the solution procedure of the step approximation, the structure and the bottom configuration were sliced into a number of shelves separated by abrupt steps. Upon applying the conservation of mass and momentum, a system of linear equations was obtained with unknown coefficients that represented the wave amplitude and the horizontal displacement of the TLS. The sparse system of linear equations was then solved by using the sparse matrix solver SuperLU. The solution was validated via the theoretical solution of the wave-scattering problem with a rectangular TLS over a flat bottom. The method was further applied to study wave scattering for different TLS geometries over uneven bottoms. Moreover, a problem with multiple TLSs was studied as well.