Lagrangian statistics of turbulent channel flow at Re$_{\tau} =$ 950 calculated with direct numerical simulation and Langevin models

We present results of Lagrangian statistical quantities for direct numerical simulation (DNS) of turbulent channel flow at Reynolds number Re$_{\tau}$ = 950 based on shear velocity and channel half-height. Attention is focused on time correlations of fluid particle velocity and on the wall-normal diffusivity as a function of the wall-normal distance. Away from the wall region the DNS results compare favorably with the results of recent statistical models based on Kolmogorov theory and Onsager symmetry relations. It is found that a value for the Kolmogorov constant of $C_0 =6$ gives optimal agreement between DNS results and results of the statistical models for all quantities considered