The Lagrangian Auto-Velocity Correlation Function

Abstract

An effective Hamiltonian method is developed to evaluate the distribution function of r_α (α=1, 2), which are the positions of the α-th particle at the time t_α. By using this method the Lagrangian auto-velocity correlation function is expressed in terms of the Eulerian one. The spectrum of the Lagrangian one clearly shows ω⁻² form under a specific model Eulerian correlation function which realizes the Kolmogorov spectrum.