Lagrangian statistics in turbulent channel flow

Lagrangian statistics have been obtained from large eddy simulations of fully developed turbulent channel flow. Calculations were performed at Reynolds numbers of 3200 and 21,900 (based on centerline velocity and channel half-width); statistics of the Eulerian velocity field are in good agreement with both direct numerical simulation data and experimental measurements. Single-particle Lagrangian velocity autocorrelations and particle mean-square dispersion were obtained from trajectories measured for 5000 fluid elements initially in either the viscous sublayer, buffer layer, or logarithmic region. The Lagrangian velocity autocorrelation of particles initially located in the log region decreases less rapidly than for particles initially in the buffer layer, which in turn decreases more slowly than for particles initially in the viscous sublayer. The ratio of the Lagrangian to Eulerian integral timescales were found to be proportional to the inverse of the turbulence intensity, in agreement with theoretical predictions and atmospheric measurements. Growth of particle mean-square dispersion at long diffusion times is proportional to time and in agreement with theory (with the exception of the surface-normal coordinate in which the presence of the channel wall limits dispersion). However, extremely long transport times are required to achieve the asymptotic state for the dispersion.