Taylor Expansions and Padé Approximations of Lagrangian and Eulerian Two-Time Velocity Correlations in Turbulence

Abstract

The time-derivatives up to the 6th-order of Eulerian and Lagrangian velocity fields in homogeneous and isotropic turbulence are computed. The Taylor expansions in powers of the time difference of the Eulerian as well as the Lagrangian two-time velocity correlations, and their Pade approximations are constructed from the time-derivatives. The Pade approximations are found to be in good agreement with direct numerical simulations.