Comparison of Classical And Weakly-singular Representations of Freesurface Potential Flows

Abstract

Within the potential-flow framework, a flow in a domain is determined in terms of the flow at the boundary surface of the flow domain by means of a classical boundary-integral representation, which defines the flow potential $\phi$ in terms of a Green function G and its gradient $\bigtriangledown G$. An alternative flow representation is the weakly-singular representation (which defines $\phi$ in terms of G and a vector Green function G associated to G via the relation $\bigtriangledown xG=\bigtriangledown G$) given by the authors for diffraction radiation by a ship advancing in regular waves. The alternative mathematical representations of far-field waves associated with the classical and weakly-singular potential representations are compared here in the special case of steady flows.