Self-similar hierarchy of coherent tubular vortices in turbulence

TL;DR

This study verifies assumptions about the energy cascade in turbulence by analyzing the self-similar hierarchy of tubular vortices across scales using direct numerical simulations, supporting a refined understanding of turbulence structure.

Contribution

It provides a quantitative verification of the vortex-based energy cascade model and demonstrates the self-similar hierarchy of coherent vortices in turbulence.

Findings

Vortex total length remains stable despite fluctuations.

Hierarchy of vortex axes is self-similar across scales.

Volume fraction of vortices is scale-independent.

Abstract

Energy transfers from larger to smaller scales in turbulence. This energy cascade is a process of the creation of smaller-scale coherent vortices by larger ones. In our recent study (Yoneda, Goto and Tsuruhashi 2021), we reformulated the energy cascade in terms of this stretching process and derived the $-5/3$ law of the energy spectrum under physically reasonable assumptions. In the present study, we provide a quantitative verification of these assumptions by using direct numerical simulations. We decompose developed turbulence in a periodic cube into scales by using the band-pass filter and identify the axes of coherent tubular vortices by the low-pressure method. Even when the turbulent kinetic energy and its dissipation rate temporally fluctuate about their temporal means, the total length of the vortices at each scale varies little with time. This result is consistent with our assumption of the temporal stationarity on the vorticity decomposition. The present numerical analysis also shows that the hierarchy of vortex axes is self-similar in a wide range of scales, i.e. in the inertial range and a lower part of the dissipation range and that the volume fraction occupied by the tubular vortices at each scale is independent of the scale.