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Identifying the tangle of vortex tubes in homogeneous isotropic turbulence

Published online by Cambridge University Press:  15 July 2019

Shiying Xiong Open the ORCID record for Shiying Xiong [Opens in a new window]  and
Yue Yang Open the ORCID record for Yue Yang [Opens in a new window]
Shiying Xiong
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China
Yue Yang*
Affiliation:
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University, Beijing 100871, PR China CAPT and BIC-ESAT, Peking University, Beijing 100871, PR China
*
†Email address for correspondence: yyg@pku.edu.cn
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Abstract

We extend the vortex-surface field (VSF), whose isosurface is a vortex surface consisting of vortex lines, to identify vortex tubes and sheets in homogeneous isotropic turbulence. The VSF at a time instant is constructed by solving a pseudo-transport equation. This equation is convected by a given instantaneous vorticity obtained from direct numerical simulation. In each pseudo-time step, we develop a novel local optimization algorithm to minimize a hybrid VSF constraint, balancing the accuracy and smoothness of VSF solutions. This key improvement makes the numerical construction of VSFs feasible for arbitrarily complex flow fields, as a general flow diagnostic tool. In the visualization of VSF isosurfaces in decaying homogeneous isotropic turbulence, the initial curved vortex sheets first evolve into vortex tubes, and then the vortex tubes are stretched and tangled, constituting a complex network. Some vortex tubes exhibit helical geometry, which suggests the important role of vortex twisting in the generation of small-scale structures in energy cascade.

JFM classification

Turbulent Flows: Isotropic turbulence Vortex Flows: Vortex dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 952 - 978
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Copyright
© 2019 Cambridge University Press 

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