Background scalar-level anisotropy caused by low-wave-number truncation in turbulent flows

We rigorously show that the truncation at low wave numbers always leads to background scalar-level anisotropy at large scales. Neither the resolution nor the spectral low-pass filter is dominant for this anisotropy, while the shape of the energy spectrum at low wave numbers is an important influence factor. Quantitative results are shown to provide references to the statistics in future postprocessing studies. Also, a simplified analytical model is introduced to explain the single-mode effects for this anisotropy.