Abstract
The fundamental problem of determining the free-surface potential flow that corresponds to a given flow at the wetted surface of a ship or offshore structure is considered for diffraction-radiation of time-harmonic waves with forward speed and the special cases corresponding to zero forward speed or zero wave frequency. Boundary-integral representations that define the velocity potential in terms of functions that are no more singular than a Green function G are given. These boundary-integral representations are weakly singular in comparison to the classical boundary-integral representations of free-surface potential flows, which define the potential in terms of G and · G.
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