Two-point enstrophy dynamics in homogeneous isotropic turbulence

TL;DR

This study investigates enstrophy dynamics in homogeneous isotropic turbulence using two-point formalism, revealing the roles of vortex stretching, diffusive transport, and the dual nature of enstrophy transfer across scales.

Contribution

It provides new insights into the multiscale enstrophy transfer mechanisms, especially the dual transfer nature linked to vortex stretching, using direct numerical simulations.

Findings

Enstrophy at scales >10η is governed by vortex stretching and diffusive transport.

Inertial enstrophy flux exhibits a dual nature with direct and reverse transfer.

Vortex stretching influences both enstrophy production and the transfer direction across scales.

Abstract

In the present work we investigate the multiscale dynamics of enstrophy in homogeneous isotropic turbulence by exploiting the two-point formalism provided by the K\'arm\'an-Howarth-Monin-Hill approach. The study is conducted on direct numerical simulations with a Taylor-based Reynolds number in the range of $140 \lesssim Re_{\lambda} \lesssim 400$. The two-point enstrophy budget at scales $r > 10 \eta$ appears to be entirely determined by production via vortex stretching, which balances enstrophy destruction, and to be dominated by the diffusive transport at smaller scales, thus preventing the emergence of a range dominated by the inertial transport of enstrophy. The decomposition in longitudinal and transverse contributions also highlights a dual nature of the inertial enstrophy flux. In particular, enstrophy appears to be transferred across scales through a non-trivial combination of direct and reverse interscale transfer. It is shown that the dual nature of this transfer is strictly related to the vortex stretching mechanism, which, in addition to producing enstrophy through vorticity amplification, also transfers longitudinal vorticity towards larger scales (by stretching the vortical elements) and transverse vorticity towards smaller scales (by contracting these vortical elements in the radial direction). The sum of these two contributions results in an overall transfer of enstrophy from large towards small scales. We propose the use of the pressure transport term as a proxy to obtain some information on the dynamics of relevant events of inertial energy and enstrophy transport. The new findings highlight the relevance of inertial compression events in longitudinal energy transport. At the same time, a good correlation between transverse energy transport events and the radial contraction of vortical elements due to vortex stretching mechanisms is also found.