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Small-scale statistics in high-resolution direct numerical simulation of turbulence: Reynolds number dependence of one-point velocity gradient statistics

Published online by Cambridge University Press:  14 November 2007

T. ISHIHARA ,
Y. KANEDA ,
M. YOKOKAWA ,
K. ITAKURA  and
A. UNO
T. ISHIHARA*
Affiliation:
Department of Computational Science and Engineering, Graduate school of Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
Y. KANEDA
Affiliation:
Department of Computational Science and Engineering, Graduate school of Engineering, Nagoya University, Chikusa-ku, Nagoya 464-8603, Japan
M. YOKOKAWA
Affiliation:
Next-Generation Supercomputer R&D Center RIKEN, 2-1-1 Marunouchi, Chiyoda-ku, Tokyo 100-0005, Japan
K. ITAKURA
Affiliation:
Super Computer System Planning and Operations Department, Japan Agency for Marine–Earth Science and Technology, 3173-25 Showa-machi, Kanazawa-ku, Yokohama 236-0001, Japan
A. UNO
Affiliation:
Next-Generation Supercomputer R&D Center RIKEN, 2-1-1 Marunouchi, Chiyoda-ku, Tokyo 100-0005, Japan
*
†Author to whom correspondence should be addressed: [email protected].
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Abstract

One-point statistics of velocity gradients and Eulerian and Lagrangian accelerations are studied by analysing the data from high-resolution direct numerical simulations (DNS) of turbulence in a periodic box, with up to 40963 grid points. The DNS consist of two series of runs; one is with kmaxη ~ 1 (Series 1) and the other is with kmaxη ~ 2 (Series 2), where kmax is the maximum wavenumber and η the Kolmogorov length scale. The maximum Taylor-microscale Reynolds number Rλ in Series 1 is about 1130, and it is about 675 in Series 2. Particular attention is paid to the possible Reynolds number (Re) dependence of the statistics. The visualization of the intense vorticity regions shows that the turbulence field at high Re consists of clusters of small intense vorticity regions, and their structure is to be distinguished from those of small eddies. The possible dependence on Re of the probability distribution functions of velocity gradients is analysed through the dependence on Rλ of the skewness and flatness factors (S and F). The DNS data suggest that the Rλ dependence of S and F of the longitudinal velocity gradients fit well with a simple power law: S ~ −0.32Rλ0.11 and F ~ 1.14Rλ0.34, in fairly good agreement with previous experimental data. They also suggest that all the fourth-order moments of velocity gradients scale with Rλ similarly to each other at Rλ > 100, in contrast to Rλ < 100. Regarding the statistics of time derivatives, the second-order time derivatives of turbulent velocities are more intermittent than the first-order ones for both the Eulerian and Lagrangian velocities, and the Lagrangian time derivatives of turbulent velocities are more intermittent than the Eulerian time derivatives, as would be expected. The flatness factor of the Lagrangian acceleration is as large as 90 at Rλ ≈ 430. The flatness factors of the Eulerian and Lagrangian accelerations increase with Rλ approximately proportional to RλαE and RλαL, respectively, where αE ≈ 0.5 and αL ≈ 1.0, while those of the second-order time derivatives of the Eulerian and Lagrangian velocities increases approximately proportional to RλβE and RλβL, respectively, where βE ≈ 1.5 and βL ≈ 3.0.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 335 - 366
Copyright
Copyright © Cambridge University Press 2007

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