Self-similar hierarchy of coherent tubular vortices in turbulence

Author:

Tsuruhashi Tomonori1ORCID,Goto Susumu2ORCID,Oka Sunao2ORCID,Yoneda Tsuyoshi3ORCID

Affiliation:

1. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8914, Japan

2. Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan

3. Graduate School of Economics, Hitotsubashi University, 2-1 Naka, Kunitachi, Tokyo 186-8601, Japan

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 2022 Nonlinearity 35 , 1380-1401), 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. This article is part of the theme issue ‘Mathematical problems in physical fluid dynamics (part 2)’.

Funder

Japan Society for the Promotion of Science

Publisher

The Royal Society

Subject

General Physics and Astronomy,General Engineering,General Mathematics

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