An experimental study of the surface elevation probability distribution and statistics of wind-generated waves

Laboratory experiments were conducted to measure the surface elevation probability density function and associated statistical properties for a wind-generated wave field. The laboratory data together with some limited field data were compared. It is found that the skewness of the surface elevation distribution is proportional to the significant slope of the wave field, §, and all the laboratory and field data are best fitted by \[ K_3 = 8\pi\S, \] with § defined as ($(\overline{\zeta^2})^{\frac{1}{2}}/\lambda_0 $, where ζ is the surface elevation, and λ₀ is the wavelength of the energy-containing waves. The value of K₃ under strong wind could reach unity. Even under these highly non-Gaussian conditions, the distribution can be approximated by a four-term Gram-Charlier expansion. The approximation does not converge uniformly, however. More terms will make the approximation worse.