Survival distribution of the stretching and tilting of vortical structures in isotropic turbulence. Anisotropic filtering analysis

TL;DR

This study investigates how anisotropic filtering affects the survival statistics of vortex stretching in isotropic turbulence, revealing scale-dependent suppression of certain structures and implications for vortex-filament-sheet relations.

Contribution

It introduces anisotropic Fourier filtering to analyze vortex stretching statistics and explores the relation between vortical structures and their scale-dependent behaviors.

Findings

Filtering large scales reduces the probability of high stretching-tilting ratios.

Removing small inertial and dissipative scales suppresses compact vortex structures.

Eigenvector alignments are affected by filtering, altering strain-vorticity interactions.

Abstract

Using a Navier-Stokes isotropic turbulent field numerically simulated (Biferale et al., Phys. Fluids (2005)), we show that the probability of having a stretching-tilting larger than twice the local enstrophy is negligible. By using an anisotropic filter in the Fourier space we analyze these survival statistics when the large, the small inertial or the small inertial and dissipation scales are filtered out. The probability that the ratio (|{\omega} \dot U|/|{\omega}|^2) is higher than a given threshold is higher in the unfiltered isotropic field than in the fields where the large scales were filtered out and is lower than in the fields were the small inertial and dissipative scales are filtered out. This is due to the suppression of compact structures in the removed ranges. 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. The study can be viewed as a test for this idea and tries to highlight its limits. 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 the angles between the strain rate tensor eigenvectors and the vorticity: eigenvector 2 reduces its alignment, while eigenvector 3 reduces its misalignment. All filters increase the gap between the most extensional eigenvalue and the intermediate one and the gap between this last and the contractile eigenvalue. When the large scales are missing, eigenvalue modulus 1 and 3 become nearly equal, similar to the modulus of the related components of the enstrophy production.