Abstract The two-dimensional hexagonal Fourier transform is introduced to reduce the background anisotropy in the numerical calculations with periodic conditions. Comparing to traditional Fourier transform with cartesian mesh, the large-scale background anisotropy is significantly reduced under different energy spectra. In addition, the phenomenon of small-scale background anisotropy is found to be related to the type of low-pass filter. Considering the standard deviation of second-order velocity correlation function with fixed two-point distance, the scaling at small scales is a result of Taylor expansion, while the scaling at large scales can be explained by using a simplified single-wavenumber analytical model. The hexagonal Fourier transform can be easily implemented by using fast Fourier transform (FFT) libraries, and is expected to be applied in future pseudo-spectral methods of two-dimensional and quasi-three-dimensional turbulent flows to minimize the background anisotropy.

中文翻译：

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在二维湍流中使用六边形傅里叶变换减少背景各向异性

摘要 在周期性条件下的数值计算中，引入二维六边形傅里叶变换来降低背景各向异性。与使用笛卡尔网格的传统傅立叶变换相比，在不同能谱下，大尺度背景各向异性显着降低。此外，发现小尺度背景各向异性现象与低通滤波器的类型有关。考虑到两点距离固定的二阶速度相关函数的标准差，小尺度的标度是泰勒展开的结果，而大尺度的标度可以用简化的单波数解析模型来解释。六边形傅里叶变换可以通过使用快速傅里叶变换 (FFT) 库轻松实现，