New nonlinear theory for a piston-type wavemaker: The classical Boussinesq equations

Abstract

In this study, we present a new nonlinear theory for a moving boundary wavemaker of piston-type based on a nonlinear dispersive shallow water model, where the classical Boussinesq equations are employed as a starting point. The new theory is inherently different from the traditional wavemaker theories, such as the usual theories employed for solving the Laplace equation equipped with the free surface boundary conditions by using the perturbation approach. To verify the wavemaker theory proposed in this study, the ratio of the wave height relative to the stroke characterizing the performance of the wavemaker was observed and compared with numerical, experimental, and Havelock's theoretical results, thereby confirming that the results obtained with the proposed theory were in significant agreement. Furthermore, a comparison of the solitary wave generated by the proposed theory and the known exact solution showed that they were in good agreement.