Ocean wave autocorrelation function

摘要

Certain models for ocean wave spectra, including the Bretschneider and Pierson-Moskowitz spectra, have spectral densities in the form of the Fréchet probability density. The autocorrelation function (ACF) of the waves is the Fourier cosine transform of the spectral density. Mellin transforms are applied to obtain the ACF in the form of a Fox H-function. If the Fréchet shape parameter is rational, the ACF may also be expressed as a Meijer G-function. These generalised functions are difficult to compute, so power series and saddle point approximations are derived to compute the ACF. The speed and accuracy of these methods is assessed.