Coherence and cross-spectral density matrix analysis of random wind and wave in deep water

Abstract

From the collected records of simultaneously measured wind and wave data during FETCH experiment, the sample and mean power spectral density and coherence functions of the fluctuating wind velocity and wave height processes are calculated. Based on the calculated mean coherence function and interaction mechanism of wind and wave, a parametric model and simple parameter estimate method are proposed to fit the coherence of the fluctuating wind velocity and wave height processes. The model is an explicit function of the main characteristic parameters of wind and wave, hence it can be used to model other empirical coherences of the random wind and wave processes in deep water. Combining the theoretical spectrum models fitting the calculated mean power spectral density functions of the fluctuating wind velocity and wave height processes and proposed coherence model for modeling the processes, the theoretical cross-spectrum density matrix of the fluctuating wind velocity and wave height processes is established. Samples of the fluctuating wind velocity and wave height processes are simulated to illustrate the influence of coherence on the random wind and wave loads.