The fast Fourier transform (FFT) technique is usually adopted in the wind field simulation based on the wavenumber-frequency joint spectrum. However, inefficient multi-dimensional FFT in both frequency and wavenumber domains are directly implemented in the existing literature. In this paper, a novel factorization method of wavenumber-frequency joint spectrum is proposed to enhance efficiency. For the one-spatial dimension wind field, the wavenumber-frequency joint spectrum is decoupled by employing the proper orthogonal decomposition technology, and it is proposed to factorize the double-index random phase angle into two independent random phase angles. Then, the previous 2D FFT can be replaced by 1D FFT. Furthermore, the proposed factorization method is extended to the two-spatial dimension wind field, considering two wavenumbers and triple-index random phase angle are introduced, the wavenumber-frequency spectrum and triple-index random phase angle are decomposed twice in succession. Thus, the undesired 3D FFT can be avoided. Simulations of a one-spatial dimension and a two-spatial dimension wind fields are used to demonstrate the accuracy and efficiency of the proposed method by comparing it with the existing method involved in multi-dimensional FFT.

中文翻译：

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基于波数-频率联合谱分解的风场高效模拟

基于波数-频率联合谱的风场模拟通常采用快速傅里叶变换（FFT）技术。然而，现有文献中直接实现了频域和波数域中低效的多维 FFT。本文提出了一种新的波数-频率联合谱分解方法来提高效率。对于一维风场，采用适当的正交分解技术对波数-频率联合谱进行解耦，提出将双指数随机相位角分解为两个独立的随机相位角。然后，可以将之前的 2D FFT 替换为 1D FFT。此外，将所提出的分解方法扩展到二维风场，考虑到两个波数和三折射率随机相位角的引入，波数频谱和三折射率随机相位角被连续分解两次。因此，可以避免不希望的 3D FFT。通过与现有的多维 FFT 方法进行比较，一维和二维风场的模拟被用来证明该方法的准确性和效率。