High-Resolution Numerical Simulation of Surface Wave Development under the Action of Wind

The paper describes the numerical experiments with a three-dimensional phase-resolving model based on the initial potential equation of motion with free surface at deep water in the periodic domain written in the surface-following nonstationary curvilinear nonorthogonal coordinate system. The numerical scheme is based on Fourier-transform method. The vertical velocity on surface is calculated by solving the three-dimensional Poisson equation for the velocity potential. The velocity potential is represented as a sum of linear and nonlinear components. The linear component is described by Laplace equation. The nonlinear component is calculated by solution of the three-dimensional Poisson equation with the iterated right-hand side. The model includes some algorithms for calculation of the energy input from wind as well as for calculation of breaking and high-frequency dissipation. Initially, the conditions are assigned as a set of small waves corresponding to JONSWAP spectrum at high wave number. In response to waves’ growth, the spectrum shifts to lower wave numbers. The evolution of spectrum is generally in an agreement with the observed data. The wave spectrum and the spectra of different rates of energy transformation as well as the statistical characteristics of wave field for different stages of development are described.