Estimates of the Relations between Eulerian and Lagrangian Scales in Large Reynolds Number Turbulence

Abstract

Abstract With Eulerian and Lagrangian spectra approximated by their “inertial subrange” forms between appropriate wave number and frequency limits, it is found that the Lagrangian integral time scale is roughly equal to the Eulerian integral length scale divided by the root-mean-square velocity. The corresponding estimate for the “microscale” ratio shows fair agreement with the large Reynolds number form of Heisen-berg's result. A similar approach to Eulerian time scales gives values approximately equal to the Lagrangian scales.