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 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.