Abstract
A new fundamental mathematical representation of linear free-surface potential flows is given. The flow representation, called velocity representation, only involves first derivatives of the Green function and defines the velocity inside a flow domain in terms of source and vortex distributions given by the normal and tangential velocity components of the velocity at the boundary surface. The velocity representation yields remarkably simple analytical representations of the waves generated by an arbitrary boundary velocity distribution for time-harmonic flows, with or without forward speed, and for steady flows.
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