The basic problem of representing farfield waves generated by an offshore structure in regular waves or a ship advancing in regular waves (or in calm water), in deep water or in uniform finite water depth, is considered. A representation that defines time-harmonic (or steady) farfield waves in terms of one-dimensional Fourier superpositions of elementary waves that satisfy the Laplace equation, the boundary conditions at the sea floor and the free surface, and the radiation condition, is given. This representation of farfield waves extend two representations given in the literature: a classical representation that does not satisfy the radiation condition, and a representation that satisfies the radiation condition but does not satisfy the Laplace equation in the nearfield.
An offshore structure in regular (time-harmonic) ambient waves generates a single system of circular waves centered at the offshore structure. The present study shows that these diverse and relatively complicated wave systems can be defined by a single, remarkably simple, generic mathematical representation that can be obtained very simply using elementary analysis based only on basic concepts. This representation of farfield waves provides considerable information and shows that—except for their amplitudes—farfield waves are entirely determined by the dispersion relation associated with the class of dispersive waves under consideration. Indeed, although farfield waves generated by a ship advancing in regular waves are primarily considered here, the approach and the analysis are valid more generally and in fact can easily be applied to a broad class of dispersive waves. The study also presents a farfield representation that defines the time-harmonic (or steady) waves generated by a ship or an offshore structure in terms of one-dimensional Fourier superpositions of elementary waves that satisfy the Laplace equation, the boundary conditions at the sea floor and the free surface, and the radiation condition.
