Reducing the background anisotropy by using hexagonal Fourier transform in two-dimensional turbulent flows

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.