Exact Nonlinear Model of Wave Generation

A numerical method for solving nonlinear hydrodynamic problems of the initial value type is developed and applied in the determination of the wave motion induced by a mechanical wave generator. The existence of a velocity potential, which satisfies the Laplace equation, is assumed. The corresponding kinetic and kinematic boundary conditions are not further simplified. A transformation of the free-surface equations is utilized. A comparison of the numerical approximation of the nonlinear solution and the observed response of a vertical-bulkhead type generator which oscillates horizontally is made. The numerical results are found to be in good agreement with the observations. The corresponding linearized problem is also solved and compared to the nonlinear approximation and observed response.