# Effects of the Reynolds number on a scale-similarity model of Lagrangian velocity correlations in isotropic turbulent flows

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## Abstract

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 \(V/V_\eta\propto{R_\lambda^{1.39}}\) obtained from the numerical data.

## Key words

turbulent mixing relative dispersion Lagrangian velocity correlation scale-similarity model dispersion velocity Reynolds number effect## Chinese Library Classification

O357.5## 2010 Mathematics Subject Classification

76F05 82C40## Preview

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