General theory of wavemaker. I. Theoretical results (Q1116822)

A general theory of the wavemaker is presented based on a recent formulation of the water wave equations by the last two authors [in: The Ocean surface, ed. by Y. Tobo and H. Mitsuyasu, Reidel (1985); pp. 17- 24]. It exploits the fact that the free surface is a surface of constant pressure in order to make the surface boundary conditions linear and to be evaluated at a fixed boundary. The main features of the present theory are as follows: First, it applies to any weakly nonlinear wavemaker. Second, the full initial-boundary value problem is solved, thus inclusing the transient effects in contrast to the classical approaches. Third, the finite amplitude (weakly nonlinear) effects are explicitly calculated. Finally, it is notable from a mathematical standpoint that the complicated second-order problem can be transformed to the form of the linear problem, and can therefore be solved by identical techniques.