O Deep Water Wave Dynamics from a General Theory of the Wavemaker.

The evolution of weakly-nonlinear water waves based on a general theory of the wavemaker is considered. The classical wavemaker problem for the velocity potential is reformulated in terms of the stream function, by introducing the pressure as an independent variable, and relegating the vertical coordinate to a dependent status. This leads to explicit forms of the linear and second-order problems, both of which are solvable in terms of nested Fourier transforms and other quadratures. The subsequent evaluation of the finite-amplitude effects has the advantage that a large part of the work is carried out by analytical means, thus avoiding difficulties common to numerical approaches and reducing computation times for quantities of physical interest.