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A vortex interaction mechanism for generating energy and enstrophy fluctuations in high-symmetric turbulence

Published online by Cambridge University Press:  12 July 2019

Tatsuya Yasuda Open the ORCID record for Tatsuya Yasuda [Opens in a new window] ,
Genta Kawahara Open the ORCID record for Genta Kawahara [Opens in a new window] ,
Lennaert van Veen  and
Shigeo Kida
Tatsuya Yasuda*
Affiliation:
Department of Physical Science and Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 466-8555, Japan Department of Aeronautics, Imperial College London, London SW7 2AZ, UK Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
Genta Kawahara
Affiliation:
Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531, Japan
Lennaert van Veen
Affiliation:
Faculty of Science, University of Ontario Institute of Technology, 2000 Simcoe Street North, Oshawa, Ontario L1H 7K4, Canada
Shigeo Kida
Affiliation:
Energy Conversion Research Center, Doshisha University, 1-3 Tataramiyakodani, Kyotanabe, Kyoto 610-0394, Japan
*
†Email address for correspondence: [email protected]
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Abstract

Turbulent vortex dynamics is investigated in triply periodic turbulent flow with Kida’s high symmetry (Kida, J. Phys. Soc. Japan, vol. 54, 1985, pp. 2132–2136) by means of unstable periodic motion representing both the statistical and dynamical properties of turbulence (van Veen et al., Fluid Dyn. Res., vol. 38, 2006, pp. 19–46). In the periodic motion, the large-scale columnar vortices, the smaller-scale vortices and the large-amplitude axial waves on the large-scale columnar vortices are detected. In terms of mutual dynamical interaction between the large-scale columnar vortices and smaller-scale vortices, we demonstrate a cyclic process of excitation of the axial waves, which leads to large-amplitude fluctuations of the total kinetic energy and enstrophy. This cyclic process is characterised by three distinct phases and is therefore reminiscent of the regeneration cycle of near-wall turbulence structures (Hamilton et al., J. Fluid Mech., vol. 287, 1995, pp. 317–348). Notably, such oscillatory behaviour is observed even in freely decaying turbulence as a consequence of the instantaneous energy transfer from smaller to larger scales.

JFM classification

Turbulent Flows: Isotropic turbulence Vortex Flows: Vortex dynamics Vortex Flows: Vortex interactions
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 874 , 10 September 2019 , pp. 639 - 676
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Copyright
© 2019 Cambridge University Press 

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Yasuda et al. supplementary movie

The time evolution of the period-5 motion in the fundamental box (0 ≦ x1, x2, x3 ≦ π/2 ). The grey, yellow, and blue-coloured isosurfaces represent low pressure, positive axial vorticity, and negative circumferential vorticity, respectively. The two-dimensional velocity vectors are also shown on the two-dimensional plane including the points O, A and (0, π/2, 0).

Download Yasuda et al. supplementary movie(Video)
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