An analysis of the initial-value wavemaker problem

A Fourier-integral method is developed to obtain transient solutions to potential wavemaker problems. This method yields solutions for wavemaker velocities which need not be given as powers of time. The results are compared with known small-time and local solutions. Examples considered include ramp, step, and harmonic wavemaker velocities. As time becomes large, the behaviour near the wave front is derived for the impulsive wavemaker, and for the harmonic wavemaker it is shown that the steady-state solution is recovered. The solution for a wavemaker velocity given as a Fourier cosine series compares favourably with available experimental results. Capillary effects are included and nonlinear effects are discussed.