Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence

We study the effect of large-scale spectral forcing on the scale-dependent anisotropy of the velocity field in direct numerical simulations of homogeneous turbulence. ABC-type forcing and helical or non-helical Euler-type forcing are considered. We propose a scale-dependent characterisation of anisotropy based on a modal decomposition of the two-point velocity tensor spectrum. This produces direction-dependent spectra of energy, helicity and polarisation. We examine the conditions that allow anisotropy to develop in the small scales due to forcing and we show that the theoretically expected isotropy is not exactly obtained, even in the smallest scales, for ABC and helical Euler forcings. When adding rotation, the anisotropy level in ABC-forced simulations is similar to that of lower Rossby number Euler-forced runs. Moreover, even at low rotation rate, the natural anisotropy induced by the Coriolis force is visible at all scales, and two distinct wavenumber ranges appear from our fine-grained characterisation, not separated by the Zeman scale but by a scale where rotation and dissipation are balanced.