Higher-order statistical analysis of short wind wave fields

Observations of along-wind surface wave profiles were made in the large Marseille-Luminy wind wave tank for a broad range of wind and fetch conditions. The processing of high resolution camera snapshots enables us to carry on a thorough statistical analysis of wind wave geometrical properties. We consider distinctively the four different wind wave fields characterized by a comprehensive image analysis in the range of capillary-gravity to gravity scales. This set of data makes it possible to describe and discuss the behavior of the distribution of wave heights, longitudinal wave slopes and curvatures in terms of their second-and higher-order moments as well as a function of the dominant wave scale. We calculate the autocorrelation and related functions and evidence the self-similar nature of wind wave fields. We also derive a simple and universal expression for the structure functions of third (skewness) and fourth (kurtosis) order which are needed for the simulation of sea radar return in the microwave regime.