An alternative expression of the time domain free surface Green function for deep water

An alternative expression of the time domain free surface Green's function is proposed. Its source and image source contribution satisfies the homogeneous Neumann condition on the mean free surface, therefore it can be useful for the boundary element method based on the double-body flow linearization. Furthermore, it is proved that it is also the solution of Clement's 4th order Ordinary Differential Equation (Clement, 1998). The Frobenius method with time step movement proposed by Chuang et al. (2007) is adopted for accurate and efficient evaluation.

Automated summary

An alternative expression for the time domain free surface Green's function is proposed, which satisfies the homogeneous Neumann condition on the mean free surface. This new expression can be beneficial for the boundary element method based on the double-body flow linearization. It is also shown to be a solution to Clement's 4th order Ordinary Differential Equation, and the Frobenius method with time step movement is used for accurate and efficient evaluation.