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A physical mechanism of the energy cascade in homogeneous isotropic turbulence

Published online by Cambridge University Press:  23 May 2008

SUSUMU GOTO
SUSUMU GOTO*
Affiliation:
Department of Mechanical Engineering and Science, Kyoto University, Yoshida-Honmachi, Sakyo, Kyoto 606-8501, Japan
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Abstract

In order to investigate the physical mechanism of the energy cascade in homogeneous isotropic turbulence, the internal energy and its transfer rate are defined as a function of scale, space and time. Direct numerical simulation of turbulence at a moderate Reynolds number verifies that the energy cascade can be caused by the successive creation of smaller-scale tubular vortices in the larger-scale straining regions existing between pairs of larger-scale tubular vortices. Movies are available with the online version of the paper.

JFM classification

Turbulent Flows: Turbulence theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 605 , 25 June 2008 , pp. 355 - 366
Copyright
Copyright © Cambridge University Press 2008

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References

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Goto supplementary movie

Movie 1. An example of the regeneration of small-scale vortices in an artificial field in which small-scale structures are removed at t=0 by low-pass filtering the Fourier modes. (Visualization of the data of a direct numerical simulation.) Light-coloured objects are the iso-surfaces of coarse-grained enstrophy at a relatively large scale (74 times the Kolmogorov length η), whereas dark-coloured objects are those at relatively small scale (18η). The size of the shown box is 200η×200η×300η. Time duration is 0<t<1.1T (where T is the integral time). It can be observed that an anti-parallel large-scale vortex pair

Download Goto supplementary movie(Video)
Video 3.7 MB

Goto supplementary movie

Movie 2. The next step of the energy cascade. Dark-coloured objects are the iso-surfaces of coarse-grained enstrophy at 18η (same as movie 1), whereas light-coloured objects are those at further smaller scale (4.5η). The size of the shown box is 130η×130η×74η. It can be observed that an anti-parallel vortex pair of 18η creates a smaller-scale vortex tube around it. Frame rate is two times lower than movie 1.

Download Goto supplementary movie(Video)
Video 922.1 KB

Goto supplementary movie

Movie 3. Smaller-scale vortex creation by larger-scale vortices in statistically stationary turbulence. Light-coloured objects are the iso-surfaces of coarse-grained enstrophy at a relatively large scale (74η), whereas dark-coloured objects are those at relatively small scale (18η). The size of the shown box is 180η×180η×300η. It can be observed that an anti-parallel vortex pair of 74η creates smaller-scale vortex tubes around it. Frame rate is the same as movie 1.

Download Goto supplementary movie(Video)
Video 3 MB