Statistical Properties of One-Dimensional Waves

Abstract

A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled wave boundary layer/sea waves model for investigation of a small-scale dynamic and thermodynamic interaction between ocean and atmosphere. The statistical properties of a nonlinear wave field are investigated on the basis of direct hydrodynamical modeling of the 1-D potential periodic surface waves. The high accuracy was confirmed by validation of the non-stationary model against known solutions and by comparison between the results obtained with different resolution in the horizontal. It is shown that the scheme allows to reproduce propagation of a steep Stokes wave for thousands of periods with a very high accuracy. The method developed is applied for simulation of the evolution of wave fields with a large number of modes for many periods of dominant waves. The statistical characteristics of a nonlinear wave field for the waves with different steepness have been investigated: spectra, curtosis and skewness, dispersion relation, and lifetime. The main result that wave field can be presented as a superposition of linear waves is valid just for small amplitudes. It is shown that a nonlinear wave field is rather a superposition of Stokes waves than that of the linear waves.