Lagrangian and Eulerian time correlations in turbulence

A dynamical analysis is made of the Lagrangian and Eulerian two-time velocity correlations QL and QE for small time difference in turbulence at very high Reynolds number. The short-time analysis yields a refinement of the so-called random sweeping model approximation for the Eulerian correlation QE. An estimate of the Lagrangian frequency spectrum of the Lagrangian correlation QL in the inertial subrange is derived on the basis of a deductive Lagrangian renormalized approximation (LRA), which is consistent with the short-time analysis. Estimates of some nondimensional constants associated with the Eulerian and Lagrangian time microscales are also obtained by making use of the energy spectrum predicted by the LRA.