Relation between Eulerian and Lagrangian Statistics

Abstract

R (x, r, t) is the Eulerian correlation function in the space with zero mean motion. R(t), the Lagrangian correlation function, may be found from the correlation function R'(x, r, t) based on the sub-ensemble of ``Eulerian trials'' for which the fluid particle at (x, r, t) is the same as that at (0, 0, 0). The hypothesis that R may be substituted for R' yields a connection between R(t) and R(x, r, t). The Lagrangian time scale is found to be about one-third the Eulerian time scale. The apparent Eulerian time scale depends on the intensity of turbulence. Data on the ratio of Lagrangian to apparent Eulerian time scales agree farily well with the analysis.