Abstract

A new two-dimensional approach to modeling of three-dimensional deep-water potential waves is given. A new approach develops a recent version of the 2-D model for 3-D waves. The 2-D model (A Heuristic Wave Model, HWM) is based on the same two-surface conditions as a 3-D model (A Full Wave Model, FWM), but instead of а 3-D elliptic equation for the velocity potential, its surface projection is used. This equation is not closed, because it contains both the vertical velocity w and its vertical derivative z w . The previous closure scheme was formulated in terms of physical (grid) variables and used some integral parameters. Contrary to that model, a new closure scheme is based on consideration of the vertical structure of Fourier amplitudes for a nonlinear component of the surface velocity w . It is shown that w and its vertical derivatives of the potential at the surface are closely connected. The coefficient in this connection is close to constant. The system of equations of a new HWM includes full surface kinematic and dynamic conditions and an additional diagnostic surface equation for calculation of the surface vertical velocity. Such transformation turns the 3-D formulation for 3-D waves into a 2-D formulation. The applicability of the 2-D model is demonstrated by comparison of the statistical results calculated by FWM and HWM for the identical set of parameters. The main advantage of the 2-D HWM is that it runs about one - two orders faster than a 3-D FWM

Keywords:3-D model of 3-D surface waves; 2-D model of 3-D surface waves; Surface vertical velocity; Input and dissipation of energy; Statistical characteristics of wave field