Statistical Properties of 3-D Waves Simulated with 2-D Phase-Resolving Model

Abstract

Further evidences of effectiveness of а two-dimensional approach to modeling of three-dimensional deep-water potential waves are given. The 2-D model is based on the same two surface conditions as 3-D, but instead of а 3-D Laplace equation (used routinely for calculation of surface vertical velocity) the surface projection of Laplace equation is suggested for use. This equation is not closed, since it contains both the vertical velocity and its vertical derivative. The closing scheme is based on consideration of vertical structure of a nonlinear component of the velocity potential. It was shown before that the surface vertical velocity and its derivative are linearly connected with a coefficient depending on some integral parameters of the problem. The applicability of the 2-D model for reproducing statistical properties of wave field was demonstrated before for relatively simple integral characteristics and spectra. The paper is devoted to comparison of more complicated statistical results generated by full 3-D model and current 2-D model. A good agreement between the high order moments for elevation and surface vertical velocity and some other characteristics proves the applicability of the model for reproducing of statistical structure of a multimode wave field with satisfactory accuracy. The main advantage of 2-D model is that it runs 30–80 times faster than a 3-D model with similar setting.