Computer Studies of Finite-amplitude Water Waves

Two numerical techniques are utilized to study the motion of two-dimensional, finite-amplitude water waves by using an electronic digital computer. The non-linear properties of water waves are of primary interest. The first part of the work introduces the Stanford-University-Modified MAC (SUMMAC) code which is proposed as a valid tool for analyzing incompressible, viscous flows with a free surface under transient conditions. The method is applied to the study of the solitary wave run-up on a vertical wall. The results are compared with the available experimental data and give a much better prediction of the wave run-up than the existing analytic theory. In the second part, Newton's process of successive corrections is applied to solve steady-state potential flows with free surface and gravity. A specific application to the analysis of solitary waves is made and all the wave characteristics are in excellent agreement with experiments. (Author).