A Dissipative Green’s Function Approach to Modeling Gravity Waves behind Submerged Bodies

Abstract

Potential flow-based methods are common in early design stages because of their associated speed and relative simplicity. By separating the resistance components of a ship into viscous and wave resistance, an inviscid method such as potential flow can be used for wave resistance determination. However, gravity waves are affected by viscosity and decay with time and distance. It has, therefore, long been assumed that the inclusion of a damping parameter in potential flow would better model the wave resistance. This article presents a Kelvin-Neumann dissipative potential flow model. A Rayleigh damping term is inserted into the Navier-Stokes equations to capture the decay of waves. A new 3D Green’s function based on the Havelock-Lunde formulation is derived by the use of a Fourier transform. An upper limit for the Rayleigh damping term is found by comparison with experiments and a possible improvement on conventional potential flow models for the wave making resistance prediction of a submerged ellipsoid is proposed.