Uniformly Valid Solutions to the Initial-Value Wavemaker Problem.

摘要

A Fourier-integral method is developed to obtain transient solutions to potential wavemaker problems. This method yields solutions that are uniformly valid 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 behavior 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 favorably with the computational and experimental results of Dommermuth et al. (1988). Capillary effects are included and nonlinear effects are discussed.