| A Lagrangian description is central to the understanding of turbulent diffusion and transport. A comprehensive numerical investigation of the Lagrangian statistics of velocity, acceleration, dissipation and other related quantities is reported, for homogeneous isotropic turbulence with no mean flow.;The algorithm is successfully applied to obtain Lagrangian velocity and velocity gradient time series from high-resolution direct numerical simulations performed on 64;The results reported include: velocity and acceleration autocorrelation functions and frequency spectra; probability density functions (pdf's) and moments of Lagrangian velocity increments; and pdf's, correlation functions and spectra of the second-order velocity-gradient invariants--dissipation (strain), enstrophy (vorticity) and "pseudo-dissipation" (deformation). Many small-scale statistics are found to be strongly Reynolds-number dependent. For instance, the acceleration variance (normalized by the Kolmogorov scales) increases as ;Extensive efforts are first made to develop an accurate and efficient algorithm to extract Lagrangian time series of velocity and velocity gradients by tracking fluid particles (of order 4,000) through numerically-calculated turbulent velocity fields obtained by the Direct Numerical Simulation method. Elaborate numerical testing shows that, provided the small scales are adequately resolved by the grid, either cubic splines or a third-order Taylor-series scheme can be used to calculate flow properties following the fluid particles by interpolation, with high accuracy. |
