Large fluctuations of the nonlinearities in isotropic turbulence. Anisotropic filtering analysis

Using a Navier–Stokes isotropic turbulent field numerically simulated in a box with a discretization of 10243 (Biferale et al., 2005), we show that the probability of having a stretching–tilting larger than a few times the local enstrophy is low. By using an anisotropic kind of filter in the Fourier space, where wavenumbers that have at least one component below a threshold or inside a range are removed, we analyze these survival statistics when the large, the small inertial or the small inertial and dissipation scales are filtered out. By considering a flow obtained by randomizing the phases of the Fourier modes, and applying our filtering techniques, we identified clearly the properties attributable to turbulence. It can be observed that, in the unfiltered isotropic Navier–Stokes field, the probability of the ratio (|ω·∇U|/|ω|2) being higher than a given threshold is higher than in the fields where the large scales were filtered out. At the same time, it is lower than in the fields where the small inertial and dissipation range of scales is filtered out. This is basically due to the suppression of compact structures in the ranges that have been filtered in different ways. The partial removal of the background of filaments and sheets does not have a first order effect on these statistics. These results are discussed in the light of a hypothesized relation between vortical filaments, sheets and blobs in physical space and in Fourier space. The study in fact can be viewed as a kind of test for this idea and tries to highlight its limits. We conclude that a qualitative relation in physical space and in Fourier space can be supposed to exist for blobs only. That is for the near isotropic structures which are sufficiently described by a single spatial scale and do not suffer from the disambiguation problem as filaments and sheets do. Information is also given on the filtering effect on statistics concerning the inclination of the strain rate tensor eigenvectors with respect to vorticity. In all filtered ranges, eigenvector 2 reduces its alignment, while eigenvector 3 reduces its misalignment. All filters increase the gap between the most extensional eigenvalue ⟨λ1⟩ and the intermediate one ⟨λ2⟩ and the gap between this last ⟨λ2⟩ and the contractile eigenvalue ⟨λ3⟩. When the large scales are missing, the modulus of the eigenvalue 1 becomes nearly equal to that of the eigenvalue 3, similarly to the modulus of the associated components of the enstrophy production.