Distributions of spatial wave size for random fields

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 derived using the Rices formulas for expected numbers of local maximum and distance from a local maximum to a level crossing countour. Review of the Rice's method to study crossing distributions will be given.