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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.

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