The Autocorrelation Function Obtained from the Pierson-Moskowitz Spectrum

This Ships and offshore structures are exposed to random wave loading in the ocean environment. When predicting the amplitude of the motion response of the ships and offshore structure, it is important to obtain the random wave loading. And the dominant load is due to wind-generated random waves. For wind-generated random waves, the ocean surface elevation is defined by ocean wave energy spectra. There are several ocean wave power spectra in which Pierson-Moskowitz spectrum is the most classical one. Pierson-Moskowitz spectrum describes the energy distribution in a fully developed sea. The power spectral density and the autocorrelation function ACF are Fourier transforms pairs. And the power spectrum is usually obtained by the Fourier transform of the of the signal. But the ACF calculation of the Pierson-Moskowitz spectrum has always been complicated and cumbersome. With the development of mathematical modeling, it is possible to explore the ACF of the wave power spectrum rapidly and efficiently, which can reasonably be considered to be of great significance to the advancement of study on numerical model of ocean wave power spectrum. Additionally, in order to verify the correctness of the result, the discrete Fourier transform is performed based on MATLAB.