Study On Free-surface Frequency Domain Green Function With Viscous Dissipation

Free-surface Green function method is widely used in solving the radiation or diffraction problems due to a ship or ocean structure oscillates on the waves. In the context of invisid potential flow, the hydrodynamic problem such as multi-body interaction and tank side-wall effect can't be well treated based on the traditional free-surface frequency domain Green function method, in which the water viscosity is omitted and the energy dissipation effect is absent. In this paper, the open-sea Green function with dissipation is presented within the theory of visco-potential flow, then the so-called tank Green function with the side-wall effect in wave tanks is formulated as a formal sum of open-sea Green functions repesenting the infinite images between two parallel side walls of the source in the tank.In this paper, the integral expression of the open-sea Green function with dissipation is formulted, then its series representation is obtained based on the pertubation solution of the dispersion equation and the transformation of partial fration to infinite series. The Green function with dissipation is decomposed into a sum of the near-field term and the far-field term, comparing to the traditional invisid Green function, the far-field term decreases much faster with a expotential decay factor introduced by the fluid viscosity, which must be particularly interesting in the solution of wave radiation and diffraction aroud one or several floating bodies.The tank Green function with dissipation constructed with singularity images can be used on evaluation of side-wall effect and supervision of the tank model test. The asymptotic part defined by the truncated infinite series is transformed into a sum including two single integrals. The analysis of the single integral and its analytical expression shows that it is finite due to the dcay factor associated with the dissipation, unlike the classical TGF which is singular at the wave numbers associated with the resonance of transversal waves between two parallel side walls. This new far-field characteristics of the tank Green function with dissipation will be crucially important for improving the validity of side-wall effects evaluation, which can be used in supervising the tank model tests.