Numerical Study on Statistical Characteristics of Developing Waves

Abstract

Long-term calculations of the evolution of three-dimensional waves ranging from the early stage to energy stabilization were made on the basis of a two-dimensional phase-resolving model. The evolution of the main integral and spectral characteristics is analyzed along with the probability distribution for the elevation field and vertical velocity. The apparent property of self-similarity (i.e. the independence of the statistical structure of the field from the degree of wave development) for the wave field on the example of the first four moments for normalized fields of elevation and surface vertical velocity is shown. The conclusion is confirmed by the calculations with a three-dimensional model.