Three dimensional wave scattering by arrays of elliptical and circular cylinders

Recently, Chatjigeorgiou and Mavrakos (2009, 2010a) provided an analytic solution for the three dimensional wave scattering by arrays of elliptical cylinders. The present paper extends the contents of the existing study to tackle the problem of the hydrodynamic interactions between elliptical and circular cylinders. The main task is to derive an analytic solution for the total velocity potential for an arbitrary body of the array and accordingly, to express the hydrodynamic pressure, the exciting forces and the wave elevation in compact analytic closed-forms.The solution method is rather complicated as it considers the circular cylinders as different geometries and not special cases of elliptical cylinders with zero elliptic eccentricity. Nevertheless, the adopted procedure enhances the mathematical reconstruction of the physical subject as it requires the derivation and the employment of addition theorems that transform expressions from elliptic to polar coordinate systems in all four possible combinations.

► The 3D wave scattering by arrays of elliptical and circular cylinders is considered.
► The study results in robust closed-form analytical solutions for the velocity potentials.
► The adopted procedure enhances the mathematical reconstruction of the physical subject.
► Expressions for the Mathieu–Bessel functions addition theorems are derived and employed.