A random-flight evaluation of the constants of relative dispersion in idealized turbulence

Abstract

In the idealized problem of homogeneous isotropic stationary inertial-range turbulence the rate of relative dispersion of an ensemble of tracer pairs can be characterized by a constantC0. In order to compute this constant with random-flight equations, however, it is necessary first to know the values of two other constants,C1andC2, that occur in the two-particle velocity-component relations of Lagrangian tracers (Faller 1992).C1andC2are found by an elaborate trial and error procedure in a new two-tracer random-flight model of dispersion that matches input and output values of these two variates. The constantC0is then computed using the Lagrangian relations and is found to be significantly smaller than when the Eulerian Kármán/Howarth correlations are used.The probability density distribution of tracer separations has a kurtosis slightly larger than that of a comparable Gaussian distribution. At small spacings the frequency of tracer spacings is six to ten times larger than would be expected from a Gaussian distribution. The distribution function for the speed of separation of the Lagrangian tracers has a negative skewness similar to that found for two-point Eulerian velocities.