Transient wavemaker theory

Unsteady waves generated in a wave channel of finite length are studied in this paper. Linear wave theory is used to formulate the problem. The Laplace transform is applied to the time and the finite Fourier cosine transform to the space coordinate to solve the corresponding initial boundary value problem. Exact analytic solutions for generations of surface waves and hydrodynamic forces on the wavemaker are presented. Examples of flap wavemaker problem are used to demonstrate present theoretical solutions. The present theory can also be used to simulate wave generations in a channel of infinite length by specifying a relatively large channel length. Comparisons of present results to those obtained by using finite element method and by analytic integral method show favorable agreement.