A Dissipative Green's Function Approach to Modeling Gravity Waves Behind Submerged Bodies

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. 1. Introduction To accurately determine the resistance is of great importance when designing a ship. Therefore, steady ship motion in calm water is a classical problem in ship hydrodynamics. Potential flow modeling is a common method to predict the wave resistance of ships. One benefit of potential flow is its computational speed. Speedy determination of the wave resistance is of great importance in early design stages. Because all ship properties are intertwined, it is not beneficial to dwell too much on one parameter. Potential flow-based models are, therefore, used for a wide range of industry applications during early phases of ship design (Wilson et al. 2010). A potential model using image sources to fulfill the free-surface condition and an exact body condition is known as a Kelvin–Neumann model. The Kelvin– Neumann problem is well known and well described, but it continues to be a topic of interest (Kuznetsov et al. 2002). Developments of Green's functions for resistance predictions is continuing to be of interest long after Michell (1898) developed his theory on the wave resistance of a ship. Recent Green's function applications include wave resistance determination (Taravella & Vorus 2012) and the calculations of forces acting on a submerged ellipsoid (Chatjigeorgiou & Miloh 2013). Doctors (2012) used a linearized potential flow method to determine the resistance components of a marine cushion vehicle.