A Two-Dimensional Approach to The Three- Dimensional Phase Resolving Wave Modeling

Abstract

A new approach to the three-dimensional modeling based on the analysis of three-dimensional equations of potential waves in the periodic domain is developed. Instead of the 3-D equation for the velocity potential, the 2-D Poisson equation on a surface is used. This equation contains both the first and second vertical derivatives of the potential. It is suggested that the equations be closed by introducing the connection between these derivatives. Finally, the model for 3-D waves includes only surface equations, which dramatically simplifies the modeling as well as provides a substantial acceleration of the calculations and reduces a volume of the memory used. The examples of integration of the equation over long periods, taking into account the input energy and dissipation, proved that such a simplified approach gives quite realistic results. It is typical that a new model runs faster by around two orders than the 3-D model