Multiscale analysis of the topological invariants in the logarithmic region of turbulent channels at $Re_{\tau}=932$

TL;DR

This study investigates the multiscale behavior of topological invariants in turbulent channel flow, revealing the limitations of traditional invariants, the influence of mean shear, and supporting vortex stretching in the energy cascade.

Contribution

It introduces a multiscale analysis of velocity gradient invariants, demonstrating the non-self-similar nature of turbulence due to mean shear effects and highlighting the role of vortex stretching.

Findings

The $R$--$Q$ plane does not capture flow changes at different scales.

Enstrophy and strain planes better represent flow dynamics.

Flow dynamics are not self-similar in the inertial range, influenced by mean shear.

Abstract

The invariants of the velocity gradient tensor, $R$ and $Q$, and their enstrophy and strain components are studied in the logarithmic layer of an incompressible turbulent channel flow. The velocities are filtered in the three spatial directions and the results analyzed at different scales. We show that the $R$--$Q$ plane does not capture the changes undergone by the flow as the filter width increases, and that the enstrophy/enstrophy-production and strain/strain-production planes represent better choices. We also show that the conditional mean trajectories may differ significantly from the instantaneous behavior of the flow since they are the result of an averaging process where the mean is 3-5 times smaller than the corresponding standard deviation. The orbital periods in the $R$--$Q$ plane are shown to be independent of the intensity of the events, and of the same order of magnitude than those in the enstrophy/enstrophy-production and strain/strain-production planes. Our final goal is to test whether the dynamics of the flow are self-similar in the inertial range, and the answer turns out to be no. The mean shear is found to be responsible for the absence of self-similarity and progressively controls the dynamics of the eddies observed as the filter width increases. However, a self-similar behavior emerges when the calculations are repeated for the fluctuating velocity gradient tensor. Finally, the turbulent cascade in terms of vortex stretching is considered by computing the alignment of the vorticity at a given scale with the strain at a different one. These results generally support a non-negligible role of the phenomenological energy-cascade model formulated in terms of vortex stretching.