Efficient Simulation of Space-Time Random Fields of Ocean Waves Using the Joint Wavenumber-Frequency Spectrum

Ocean waves are random and vary in space and time. Thus, the simulation of the space–time random field of ocean waves and related processes feature in many applications, such as the prediction of the extreme wave crest over an area. The spectral representation method is widely adopted to generate time series for random waves at one spatial location. Although this approach can be used for point-by-point simulation over multiple locations, it is computationally prohibitive for large number of discrete points. This paper presents a new efficient and accurate method for simulating random wave processes for an arbitrarily large number of points. The method treats space and time as a continuous Gaussian random field and employs the wavenumber-frequency spectrum to generate the time series simultaneously and efficiently over a large region by invoking the two-dimensional fast Fourier transform technique. One unique characteristic of ocean waves is that the dispersion relationship confines the energy to a curve in the wavenumber-frequency plane that is described by a Dirac delta function, which is unsmooth. This is resolved by using a Gaussian kernel function to ensure high fidelity of the wavenumber-frequency spectrum. The proposed method is versatile and can be applied to simulate processes related to ocean waves, including the wave elevation, wave particle kinematics, and dynamic pressures. Its accuracy and effectiveness are demonstrated through an assortment of engineering applications.