Different approaches to numerical modeling of sea waves

The main approaches in direct modeling of surface waves based on complete equations of dynamics of the inviscid liquid with a free surface are briefly considered. Most of the models are intended for study of the applied and engineering problems. It is assumed that the main model is written in the curvilinear coordinate system where the height is counted off from wave surface. In the two-dimensional periodic formulation, when using a conformal system, the problem is reduced to the system of one-dimensional equations that can be easily solved using Fourier-transform method. For three-dimensional waves such simplifications do not exist, thus, the vertical velocity on the surface is calculated by solving a three-dimensional Poisson equation or using a surface integral method. An approximate scheme based on the two-dimensional equations is considered. The scheme allows reproducing the statistical mode of waves with high accuracy consistent with the similar results obtained from the accurate three-dimensional model.