Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

Abstract

Lagrangian statistics have been obtained from direct numerical simulations of isotropic turbulence and homogeneous shear flow. Quantities presented include properties of the dispersion tensor 〈Xi(t)Xj(t)〉, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The dispersion measurements from the simulations of isotropic turbulence are in good agreement with those of Warhaft [J. Fluid Mech. 144, 363 (1984)] and Stapountzis et al. [J. Fluid Mech. 165, 401 (1986)]. ‘‘Integral’’ time scales were defined as the time required for the temporal correlations to decrease to 1/e of their initial value. The ratio of TeL/TeE from the simulations of isotropic turbulence was approximately 0.8, in good agreement with the data of Sato and Yamamoto [J. Fluid Mech. 175, 183 (1987)]. The principal angle of 〈Xi(t)Xj(t)〉 from the shear flow simulations shows reasonable agreement with a similar study done by Riley (Ph.D. dissertation, The Johns Hopkins University, Baltimore, 1971). The Lagrangian time microscale was found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame. A comparison made between the measured diffusivity tensor and measurements of Tavoularis and Corrsin [Int. J. Heat Mass Transfer 28, 265 (1985)] show reasonable agreement.