Lagrangian Statistics from Numerically Integrated Turbulent Shear Flow

Abstract

Lagrangian turbulence statistics were obtained from a three-dimensional numerical model of plane Poiseuille flow at large Reynolds number. Single-particle Lagrangian correlations were computed and compared with Eulerian space correlations. Although the curves were not self-similar, a dimensionless scale ratio defined at the e-folding time was comparable to Eulerian-Lagrangian scale ratios found in the literature. The numerically obtained mean-square particle displacements exhibited correct short- and long-time behavior. Mean-square particle separations were analyzed, and two-particle Lagrangian velocity correlations taken at the same time were more persistent than Lagrangian autocorrelations. A semiempirical functional form was constructed for the two-particle velocity correlations which yielded two-particle distance correlations in good agreement with those of the numerical model. The effect of mean shear on downstream separation was examined. Results indicate a t3 or steeper dependence for downstream mean-square separation 〈(xa − xb)2〉, with strong shear and Reynolds stress. Batchelor's similarity law, namely, that 〈(xaj − xbj)2〉 ∝ εt3 in directions not controlled by shear, is postulated for the direction of shear when shear generates ε. This postulate was tested numerically and found to be consistent.