Energy transfer and vortex structures: Visualizing the incompressible turbulent energy cascade

TL;DR

This study compares energy transfer mechanisms in homogeneous isotropic turbulence and vortex tube interactions, revealing differences in structure organization and transfer processes, and highlighting the impact of flow type on energy cascade dynamics.

Contribution

It provides a detailed visualization and analysis of energy transfer in both steady HIT and vortex interactions, emphasizing the distinct behaviors and structures involved.

Findings

No significant correlation between energy transfer regions and vorticity in HIT.

Simpler organization of structures in vortex tube interactions.

Energy transfer mechanisms differ between steady HIT and vortex reconnection flows.

Abstract

The transfer of kinetic energy from large to small scales is a hallmark of turbulent flows. Yet, a precise mechanistic description of this transfer, which is expected to occur via an energy cascade, is still missing. Several conceptually simple configurations with vortex tubes have been proposed as a testing ground to understand the energy cascade. Here, we focus on incompressible flows and compare the energy transfer occurring in a statistically steady homogeneous isotropic turbulent (HIT) flow with the generation of fine-scale motions in configurations involving vortex tubes. We start by filtering the velocity field in bands of wavenumbers distributed logarithmically, which allows us to study energy transfer in Fourier space and also visualize the energy cascade in real space. In the case of a statistically steady HIT flow at a moderate Reynolds number, our numerical results do not reveal any significant correlation between regions of intense energy transfers and vorticity or strain, filtered in corresponding wavenumber bands, nor any simple self-similar process. In comparison, in the transient turbulent flow obtained from the interaction between two antiparallel vortex tubes, we observe a qualitatively simpler organization of the intense structures, as well as of the energy transfer. The process leading to vortex reconnection via flattening of interacting vortex cores in two intense ribbons of vorticity, also appears as qualitatively different from the physics of HIT. Our results indicate that the specific properties of the transient flows affect the way energy is transferred, and may not be representative of HIT.