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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): \phi

in terms of a Green function G and its gradient Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): \bigtriangledow G

. An alternative flow representation is the weakly-singular representation (which defines Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): \phi

in terms of G and a vector Green function G associated to G via the relation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://mathoid.scipedia.com/localhost/v1/":): \bigtriangledow xG = \bigtriangledow 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.