Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows
A scale-similarity model of a two-point two-time Lagrangian velocity correlation (LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows (HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic a...
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Published in | Applied mathematics and mechanics Vol. 39; no. 11; pp. 1605 - 1616 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Shanghai
Shanghai University
01.11.2018
Springer Nature B.V School of Engineering Science, University of Chinese Academy of Sciences,Beijing 100049, China%State Key Laboratory of Nonlinear Mechanics(LNM), Institute of Mechanics,Chinese Academy of Sciences, Beijing 100190, China School of Engineering, Sun Yat-sen University, Guangzhou 510275, China State Key Laboratory of Nonlinear Mechanics(LNM), Institute of Mechanics,Chinese Academy of Sciences, Beijing 100190, China |
Edition | English ed. |
Subjects | |
Online Access | Get full text |
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Summary: | A scale-similarity model of a two-point two-time Lagrangian velocity correlation (LVC) was originally developed for the relative dispersion of tracer particles in isotropic turbulent flows (HE, G. W., JIN, G. D., and ZHAO, X. Scale-similarity model for Lagrangian velocity correlations in isotropic and stationary turbulence.
Physical Review E
,
80
, 066313 (2009)). The model can be expressed as a two-point Eulerian space correlation and the dispersion velocity
V
. The dispersion velocity denotes the rate at which one moving particle departs from another fixed particle. This paper numerically validates the robustness of the scale-similarity model at high Taylor micro-scale Reynolds numbers up to 373, which are much higher than the original values (
R
λ
= 66, 102). The effect of the Reynolds number on the dispersion velocity in the scale-similarity model is carefully investigated. The results show that the scale-similarity model is more accurate at higher Reynolds numbers because the two-point Lagrangian velocity correlations with different initial spatial separations collapse into a universal form compared with a combination of the initial separation and the temporal separation via the dispersion velocity. Moreover, the dispersion velocity V normalized by the Kolmogorov velocity
V
η
≡
η
/τ
η
in which
η
and τ
η
are the Kolmogorov space and time scales, respectively, scales with the Reynolds number
R
λ
as
V
/
V
η
∝
R
λ
1.39
obtained from the numerical data. |
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ISSN: | 0253-4827 1573-2754 |
DOI: | 10.1007/s10483-018-2387-6 |