Abstract
Spectral wave modelling is widely used to simulate large-scale wind–wave processes due to its low computation cost and relatively simpler formulation, in comparison to phase-resolving or hydrodynamic models. However, some applications require a time-domain representation of sea waves. This article proposes a methodology to transform the wave spectrum into a time series of water surface elevation for applications that require a time-domain representation of ocean waves. The proposed method uses a generated phase spectrum and the inverse Fourier transform to turn the wave spectrum into a time series of water surface elevation. The consistency of the methodology is then verified. The results show that it is capable of correctly transforming the wave spectrum, and the significant wave height of the resulting time series is within 5% of that of the input spectrum.
Highlights
The proposed method uses a generated phase spectrum and the inverse Fourier transform to turn the wave spectrum into a time series of water surface elevation
The transformation of a function from frequency to time domain is usually done with an inverse Fourier transform (IFT)
The box plots show that, except in the case of outliers, the significant wave height of the generated time series of η will remain within 5 % of the spectral significant wave height, showing that the transformation from the spectrum to the time series does not influence the underlying sea state
Summary
The transformation of a function from frequency to time domain is usually done with an inverse Fourier transform (IFT). When feeding a real-valued function, such as a time series of water surface height, to the Fourier transform, the result is a complex-valued function that represents the Fourier coefficients of that function With these coefficients, it is possible to obtain the variance spectrum of such function with:. Where F ( x ) is the Fourier transform of the function x, and F ( x ) denotes the absolute value of the given complex variable, in this case, F ( x ) Another point to note is that due to the symmetry of the Fourier transform’s result, the second half of S is equal to the first half, mirrored, the first half is usually multiplied by two and the second discarded, making the spectrum one-sided
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