LES computation of Lagrangian statistics in homogeneous stationary turbulence; Application of universalities under scaling symmetry at sub-grid scales

In this paper, the turbulent cascade with intermittency is presented in the framework of universalities of eddy fragmentation under scaling symmetry. Based on these universalities, the stochastic estimation of the velocity increment at sub-grid scales is introduced in order to simulate the response of light solid particle to inhomogeneity of the flow at small spatial scales. The LES of stationary box turbulence was performed, and the computed Lagrangian statistics of tracking particle was compared with measurements. The main effects from recent experimental study of high Reynolds number stationary turbulence are reproduced by computation. For the velocity statistics, the numerical results were in agreement with classical Kolmogorov 1941 phenomenology. However the distribution of velocity increment, computed at different time lag, revealed the strong intermittency: at time lag of order of integral time scale, the velocity increment was distributed as Gaussian, at small time lags this distribution exhibited the long stretched tails.