An Analytical Solution of Transient Wave Generation in the Wave Channel

Abstract

Transient characteristics of wave generation in the wave channel can provide unique and important information in contrast to the steady and periodic motion of propagation waves. In this paper, a new analytical solution is proposed for a transient wavemaker problem in the wave channel. The mathematical model of the wavemaker problem is established based on the linear potential wave theory, and a new analytical solution for the corresponding initial and boundary-value problem is presented. The present solution methodology is motivated and developed from old methods shown in literature. The present solution can be mathematically reformulated and shown to be identical to the previous solution using different solution methodology. The present analytical solution is further compared with numerical results and experiments to validate the mathematical model. The present solution is used to calculate the steady state generated wave forms that compare very well with the steady wave theory both in wave length and wave period. The present solution is also used to study unsteady characteristics of wave heights and wave lengths of the leading waves. The present analytical solution methodology can provide an easier approach to obtain the analytical solution for transient wave generation problem in the wave channel.