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

Abstract : We study the effect of large-scale spectral forcing on the scale-dependent anisotropy of the velocity field in direct numerical simulations of homogeneous incompressible turbulence. Two forcing methods are considered: the steady ABC single wavenumber scheme and the unsteady non-helical or helical Euler scheme. The results are also compared with high resolution data obtained with the negative viscosity scheme. A fine-grained characterization of anisotropy, consisting in measuring some quantities related to the two-point velocity correlations, is used: we perform a modal decomposition of the spectral velocity tensor into energy, helicity and polarization spectra. Moreover, we include the explicit dependence of these three spectra on the wavevector direction. The conditions that allow anisotropy to develop in the small scales due to forcing alone are clearly identified. It is shown that, in turbulent flows expected to be isotropic, the ABC forcing yields significant energy and helicity directional anisotropy down to the smallest resolved scales, like the helical Euler scheme when an unfavourable forcing scale is used. The direction-and scale-dependent anisotropy is then studied in rotating turbulence. It is first shown that, in the ABC-forced simulations the slope of the energy spectrum is altered and the level of anisotropy is similar to that obtained at lower Rossby number in Euler-forced runs, a result due both to the nature of the forcing itself and to the fact that it allows an inverse cascade to develop. Second, we show that, even at low rotation rate, the natural anisotropy induced by the Coriolis force is visible at all scales. Finally, we identify two different wavenumber ranges in which anisotropy behaves differently, and show that the characteristic lenghscale separating them is not the Zeman scale. If the Rossby number is not too low, this scale is the one at which rotation and dissipation effects balance.
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Donato Vallefuoco, Aurore Naso, Fabien Godeferd. Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence. Journal of Turbulence, Taylor & Francis, 2018, 19, pp.107-140. ⟨10.1080/14685248.2017.1400667⟩. ⟨hal-01630158⟩

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