Revision as of 11:07, 6 July 2020

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 ${\displaystyle \phi }$ in terms of a Green function ${\displaystyle G}$ and its gradient ${\displaystyle \bigtriangledown G}$. An alternative flow representation is the weakly-singular representation (which defines ${\displaystyle \phi }$ in terms of ${\displaystyle G}$ and a vector Green function ${\displaystyle G}$ associated to ${\displaystyle G}$ via the relation ${\displaystyle \bigtriangledown xG=\bigtriangledown G}$) 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.