LAGRANGIAN VELOCITY AUTOCORRELATION IN ISOTROPIC TURBULENCE

An analysis is made of the Lagrangian and the Eulerian velocity autocorrelations R(L) (s,t) and R(E) (s,t) at times s and t for small time lag tau = s - t in isotropic decaying turbulence, and it is shown that under appropriate conditions R(E) less-than-or-equal-to R(L) for small tau in three dimensions, irrespective of the form of the energy spectrum. The behaviors of R(E) and R(L) not limited to small tau are studied by direct numerical simulations in two dimensions. The values of R(L) obtained by the Lagrangian renormalized approximation are found to be in good agreement with the simulations and with the existing data of three-dimensional simulations and experiments.