Spatial size of waves

Abstract

A method of measuring three-dimensional spatial wave size is proposed and statistical distributions of the size characteristics are derived in explicit integral forms for Gaussian sea
surfaces. New definitions of wave characteristics such as the crest-height, the length, the size and the wave front location are provided in fully dimensional context. The joint statistical
distributions of these wave characteristics are expressed in the terms of a directional power  spectrum. The proposed approach allows for investigation of the influence of spectral shape and
directionality on the joint distributions of the size characteristics. The method is validated by comparing numerical evaluations of the distributions with the observed frequencies extracted from
simulations of sea surface. The comparisons demonstrate
high accuracy of the obtained distributions.