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==Abstract== | ==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 <math>\phi</math> in terms of a Green function G and its gradient <math>\bigtriangledown G</math>. An alternative flow representation is the weakly-singular representation (which defines <math>\phi</math> in terms of G and a vector Green function G associated to G via the relation <math>\bigtriangledown xG = \bigtriangledown G</math>) 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. | + | 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 <math>\phi</math> in terms of a Green function <math>G</math> and its gradient <math>\bigtriangledown G</math>. An alternative flow representation is the weakly-singular representation (which defines <math>\phi</math> in terms of <math>G</math> and a vector Green function <math>G</math> associated to <math>G</math> via the relation <math>\bigtriangledown xG = \bigtriangledown G</math>) 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. |
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 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 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/":): 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/":): \bigtriangledown 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 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/":): G
and a vector Green function 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/":): G
associated to 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/":): 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/":): \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.
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Published on 01/01/2005
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