The computation of forward speed Green function in cylindrical coordinate system

Recently, a Rankine-Kelvin hybrid method based on meshless cylinder control surface has been developed to solve the ship seakeeping with forward-speed problem. In the external domain, the integration of forward speed Green function needs to be calculated on the cylinder control surface. However, the current computation methods of forward speed Green function are most based on studies in Cartesian coordinate system and not convenient to be integrated on the cylindrical surface. The forward speed Green function and its derivatives are then studied in cylindrical coordinate system in this paper. The double Fourier integral written in tow-fold polar and wavenumber integral is analysed. The polar integral is first performed by using the theorem of residues unlike the classical formulation in which the wavenumber integral was performed before the polar integral. The resultant wavenumber integral is reformulated by removing the weak singularities and evaluated numerically. The numerical results are validated through comparison with those calculated in Cartesian coordinate system, and the wave contours due to a translating pulsating source submerged below the free surface of infinite water depth are given.