The hydrodynamics of arrays of truncated elliptical cylinders

The hydrodynamic scattering problem by arrays of elliptical truncated cylinders subjected to regular waves is investigated. Linear potential theory is employed that is based on the assumption of inviscid/incompressible fluid and irrotational flow. Effort is made to provide an analytical solution of the associated hydrodynamic boundary value problem. The solution is based on the semi-analytical formulation of the diffraction potentials and the application of the so-called Mathieu functions addition theorem. The latter is decomposed into even and odd Mathieu functions whereas it considers arbitrary angular orientations of the semi-major axes of the bodies. It was also extended to account for negative Mathieu parameters which correspond to the infinite real roots of the transcendental equation. The details of the interaction phenomena are investigated with the aid of the transfer functions of the exciting forces on two-body configurations. Indicative results for the free surface elevation around the bodies are also provided.